AMNA NAWAZ: A top aide to Ukrainian President Volodymyr Zelenskyy today called this weekend's Ukraine peace conference a success.

It was derided just as definitively by the Kremlin as ineffective.

Russia was not invited.

More than 90 nations attended the summit in the Swiss Alps.

Nick Schifrin sat down yesterday with U.S. National Security Adviser Jake Sullivan, who accompanied Vice President Kamala Harris.

Last night, "PBS News Weekend" aired part one of that conversation.

Tonight, part two begins on the front lines in Eastern Ukraine.

NICK SCHIFRIN: Jake Sullivan, thank you very much.

Welcome to the "NewsHour."

JAKE SULLIVAN, U.S. National Security Adviser: Thanks for having me.

NICK SCHIFRIN: Does the agreement that you have made with Ukraine to allow Ukraine to fire American weapons just over the border into Russia at Russian forces that are about to attack into Ukraine, does that extend beyond the Kharkiv region, including into the Sumy region, where Russian forces have also been targeting Ukraine?

JAKE SULLIVAN: It extends to anywhere that Russian forces are coming across the border from the Russian side to the Ukrainian side to try to take additional Ukrainian territory.

NICK SCHIFRIN: So, that could include the Sumy region?

JAKE SULLIVAN: That's happened in Kharkiv.

We have seen initial indications that Russia has made exploratory moves across in Sumy.

And so it would apply there as well.

This is not about geography.

It's about common sense.

If Russia is attacking or about to attack from its territory into Ukraine, it only makes sense to allow Ukraine to hit back against the forces that are hitting it from across the border.

NICK SCHIFRIN: Of course, Russia is attacking Ukraine from all parts of Russia.

Why draw the line there?

This week's bilateral security agreement obliges the U.S. to -- quote -- "support Ukraine's efforts to win today's war."

How do you expect Ukraine to win if it can't attack Russian forces that use Russia itself as a sanctuary?

JAKE SULLIVAN: Well, first, we are permitting Ukrainian forces to attack Russian forces using Russia as a sanctuary in the areas where on the battlefield they are attacking from inside Russia with artillery, with other ground-based munitions.

Second, we have made clear -- and we have seen over the course of the past two years Ukraine do this -- that they can use air defense systems, including those supplied by the United States, to take Russian planes out of the sky, even if those Russian planes are in Russian airspace, if they're about to fire into Ukrainian airspace.

(CROSSTALK) NICK SCHIFRIN: Right.

Ukraine has suggested publicly that the F-16s they will begin to operate in the near future will be based outside of Ukraine.

Is that the plan, to put the F-16s in a NATO country?

JAKE SULLIVAN: The plan is to put the F-16s in Ukraine.

And the bilateral security agreement that the president and President Zelenskyy signed reinforced this point, that we want to help Ukraine have this capability.

It should be a capability based in Ukraine.

NICK SCHIFRIN: The bilateral security agreement obliges the U.S. for 10 years to share weapons, intelligence-sharing, long-term training, joint weapons production.

You struggled to get the supplemental through Congress.

Joe Biden might not be the president next year, and former President Trump has questioned whether the U.S. should continue to support military aid and other aid to Ukraine.

Why make a commitment that you don't know whether the U.S. can keep?

JAKE SULLIVAN: Well, first, I do believe the U.S. will keep it.

There is a strong bipartisan majority for supporting Ukraine in both the House and the Senate and among the American public.

And that majority was actually reflected in the vote on the supplemental, more than 300 votes in the House, more than 70 votes in the Senate.

And I believe that that is an enduring commitment that we see from both parties, and it will ultimately shine through.

NICK SCHIFRIN: It's dangerous to ever assume what former President Trump would do if he were reelected, but there's no guarantee that he will respect the bilateral security agreement, right?

JAKE SULLIVAN: In life in general and in democracy in particular, there are never any absolute lock, stock guarantees.

Things can change, leaders can change, situations can change.

All President Biden can do is set a course and a vision for what is in the United States' national security interest, what is in the interest of the transatlantic alliance, and what is in the interest of our partnership with Ukraine.

And that type of approach has historically served America well.

And President Biden is going to stick with that approach for as long as he is president of the United States, which he, of course, expects to be for another four years.

NICK SCHIFRIN: Let me switch to Israel.

Indirect negotiations between Israel and Hamas have resumed this past week after Hamas formally replied to the road map that President Biden laid out.

A regional official tells me that Hamas is asking for a timeline of a permanent cease-fire and an Israeli withdrawal from Gaza.

The road map that's been laid out only obliges Israel to have a temporary cease-fire that would continue so long as negotiations were continuing.

Is that Hamas' proposed change dead on arrival?

JAKE SULLIVAN: I don't think that the current proposal just obliges a temporary pause.

It is a road map, as the president said in his remarks at the end of May, to an end to the war.

Now, it's true, the first phase is set out six weeks.

And in those six weeks, the goal is to negotiate the necessary conditions to put in place a permanent cessation of hostilities.

And that formula, permanent cessation of hostilities, is in the proposal that was sent to Hamas.

Now, if within the six weeks, all of those conditions aren't agreed indirectly between Israel and Hamas, then they stay at the negotiating table and the cease-fire remains in place.

NICK SCHIFRIN: And that is what's different about this proposal, that Israel is committed to continuing that temporary cease-fire so long as negotiations continue.

JAKE SULLIVAN: That's right.

Now, Hamas has come back with changes to the agreement.

I wouldn't characterize it exactly as you have just put it, but it is certainly the case that they are looking for a move from phase one to phase two that gives them a sense that there will actually be a permanent end to hostilities.

Now... NICK SCHIFRIN: And is that dead on arrival, or is that a possibility?

JAKE SULLIVAN: From my perspective, this is a negotiation.

Israel authorized a proposal to be put forward.

Hamas has come back with some elements that, in our view, are understandable, not unanticipated, and other elements that are out of step with what the U.N. Security Council set forward and what was in President Biden's speech.

Now there needs to be a back-and-forth.

And we need to bridge the remaining gaps and get to a conclusion.

NICK SCHIFRIN: Do you believe Hamas leader Yahya Sinwar considers the many Gazans who have died -- quote -- "necessary sacrifices" that would create worldwide pressure on Israel, as The Wall Street Journal reported recently he told mediators?

JAKE SULLIVAN: So, I have not heard that specific phrase, other than reading it in The Wall Street Journal.

But I will tell you... NICK SCHIFRIN: Has he expressed something similar, even if he... (CROSSTALK) NICK SCHIFRIN: ... that language?

JAKE SULLIVAN: ... that I am concerned -- I am concerned that Sinwar and other Hamas leaders are making a crude and cynical calculus with the lives of innocent Palestinian people.

And I think the best way to prove that, in fact, they do care about the lives and the well-being of Palestinian civilians is to agree to a cease-fire.

NICK SCHIFRIN: There's a lot of concern that, on the Israeli side, Benjamin Netanyahu is either unwilling or unable to get this deal through the current coalition.

Are you worried both sides are more interested in blaming the other for failure, rather than actually making progress?

JAKE SULLIVAN: Look, in any negotiation, there's a risk of that kind of dynamic taking hold.

But I will tell you, the Israeli government has remained steadfast in standing behind the proposal that was put forward in May.

It has not walked away from it.

NICK SCHIFRIN: The Israeli government.

You mean the prime minister himself or... JAKE SULLIVAN: The prime minister has not walked away from it, has not picked up the phone and said to President Biden, hey, by the way, I'm backing off this thing.

He has stood by it.

NICK SCHIFRIN: He stood by it not so much publicly, but you have said repeatedly and the secretary of state says repeatedly, privately, he has reassured you guys, that, yes, he's behind this proposal, right?

JAKE SULLIVAN: That is correct.

And if Hamas took that proposal tomorrow, I believe that proposal would go into effect.

NICK SCHIFRIN: Are you concerned at all that Netanyahu is extending the war in order to stay in power or to wait until the November U.S. election?

JAKE SULLIVAN: Look, I have learned long ago not to characterize the motives of leaders, to only judge them by their actions.

And the action I see is an Israeli prime minister who authorized a proposal to be put forward that President Biden laid out for the world, that the U.N. Security Council endorsed, and, if Hamas would take it, Israel would take it.

NICK SCHIFRIN: Israel is making progress in Rafah.

Do you believe that puts pressure on Israel not only to agree to a cease-fire, but also to talk more concretely about the day-after plan?

JAKE SULLIVAN: There will come a moment when the shift from major military operations to some other reality is going to have to take place, and that may be sooner, rather than later.

NICK SCHIFRIN: Finally, bringing us back to Ukraine and the summit, the peace that the world and the U.S. and you have been speaking about for the last 24 hours here is in part about respecting the principles of international law.

The State Department recently concluded it's reasonable to assess U.S. weapons have been used by Israel since October the 7th inconsistent with its international humanitarian law obligations.

Is there a U.S. double standard?

JAKE SULLIVAN: President Biden has enunciated the same principle when it comes to Israel that he has enunciated with respect to Ukraine.

Israel has a right to defend itself against a vicious and brutal terrorist organization, but it has a responsibility, even despite the burden of having to fight Hamas in hospitals and schools, to do the utmost to protect civilians.

And our position with respect to Russia and Ukraine is that Russia has no right whatsoever to invade a sovereign country, cause harm, and operate in utter and complete flagrant violation of the U.N. charter.

What the president is most concerned about is the human dimension of each of these conflicts.

And that sense of motivation to try to bring peace and security on the basis of a fair and just outcome in both Gaza and in Ukraine, that's something that motivates him every day.

NICK SCHIFRIN: Jake Sullivan, thank you very much.

JAKE SULLIVAN: Thanks for having me.