AMNA NAWAZ: Saudi Arabia and Iran are taking a major step to improve relations.

At a gathering in China today, the two nations agreed to reopen embassies in each other's capitals.

In nearly a decade, the first formal meeting between longtime rivals.

Saudi TV showed the foreign ministers from Iran and Saudi Arabia signing a landmark deal brokered by Beijing to reestablish diplomatic relations.

Chinese spokeswoman Mao Ning said the deal could bring peace to the Middle East.

MAO NING, Chinese Foreign Ministry Spokeswoman (through translator): The further improvement of Saudi-Iranian relations fully demonstrates the willingness and ability of regional countries to take the lead in regional peace and development.

AMNA NAWAZ: The agreement includes the resumption of flights between Saudi Arabia and Iran, the reopening of embassies and consulates, bilateral visits, and the granting of visas for citizens of the two countries.

The deal comes a month after Riyadh and Tehran announced they would normalize relations in a diplomatic breakthrough that represents Beijing's growing influence in the region.

Relations between the two nations have been fraught for decades, but officially broke in 2016, when Saudi Arabia carried out a mass execution of nearly 50 people, including prominent Shiite cleric Sheik Nimr al-Nimr.

In response, Iranian protesters stormed the Saudi Embassy in Tehran, and Riyadh lashed back.

ADEL AL-JUBEIR, Saudi Arabian Foreign Minister (through translator): The kingdom, in light of these realities, announces the cutting of diplomatic relations with Iran and requests the departure of delegates of diplomatic missions.

AMNA NAWAZ: Another thorn in the relationship, the war in Yemen.

For eight years, Saudi Arabia and Iran have backed opposite sides of a brutal battle that's killed hundreds of thousands.

In 2014, Houthi rebels, backed by Tehran, seized the capital and took over much of the country.

In 2015, Iran's Sunni archrival, Saudi Arabia, mobilized a coalition of Arab militaries to defeat the group.

The man behind Saudi Arabia's strategy, de facto ruler Mohammed bin Salman, known as MBS, who served as defense minister when the war broke out.

But the U.S. last month also expressed optimism that the deal between Iran and Saudi Arabia could be positive.

KARINE JEAN-PIERRE, White House Press Secretary: We welcome any efforts to help end the war in Yemen and de-escalate tensions in the Middle East region.

AMNA NAWAZ: For decades, the U.S. and Saudi Arabia had close relations, but those deteriorated over the kingdom's human rights record.

QUESTION: Jamal Khashoggi, will you apologize to his family, sir?

AMNA NAWAZ: And hit a new low in 2018, when journalist Jamal Khashoggi walked into the Saudi Consulate in Istanbul, was murdered and dismembered.

The U.S. intelligence community assessed the operation was approved by MBS himself.

The following year, candidate Joe Biden promised punishment.

JOE BIDEN, President of the United States: We are going to in fact make them pay the price and make them in fact the pariah that they are.

AMNA NAWAZ: Meanwhile, news of a rapprochement between Saudi Arabia and Iran has sent shockwaves through the region and dealt a blow to Israeli Prime Minister Netanyahu, who's made the threat posed by Iran a personal crusade and had hoped for a deal with the kingdom.

BENJAMIN NETANYAHU, Israeli Prime Minister: The ability to fashion normalization and a formal peace with Saudi Arabia will be a quantum leap, because I think it will change Israel's relationship with the rest of the Arab world.

AMNA NAWAZ: For more on this, we turn to Vali Nasr.

He was an adviser at the State Department during the Obama administration and is now a professor at the Johns Hopkins University's School of Advanced International Studies.

Vali Nasr, welcome back to the "NewsHour."

Before we get into the details of this and the potential impact, just put this into context for us.

How big of a deal is it that these two nations are working to normalize relations?

VALI NASR, School of Advanced International Studies, Johns Hopkins University: I think it's very important for the Middle East.

This -- the sour relations between the two was viewed as the most important cleavage in the region.

And it also pushed the Arabs towards Israel in an alliance against Iran.

So, the fact that they decided to mend fences really reshapes the entire way in which the Middle East functions.

AMNA NAWAZ: Let's talk about some of those impacts, then.

What does the rapprochement between Iran and Saudi Arabia in particular mean for some of those proxy conflicts that we mentioned in the report, in Yemen and Lebanon and elsewhere?

VALI NASR: Well, the very first place that it's going to have an impact is in Yemen, which -- and, today, also, there were rumors that the Houthis are going to extend their cease-fire until December 2023.

Saudi Arabia has been engaged in talks with the Houthis.

It wants Iran to stop supplying Houthis with weapons, put political pressure on the Houthis to agree to a political end to the war.

And the thawing of the relations between them makes all of that much more possible.

And then, if there is success in Yemen, then we can think about Syria and Lebanon and Iraq as well.

AMNA NAWAZ: What does this new establishment mean for American and Israeli efforts, in particular, to isolate Iran, to have sanctions on Iran, to contain Iran's nuclear program?

What does that mean?

VALI NASR: Well, for the United States, its policy has been somewhat schizophrenic.

On the one hand, it wants de-escalation in the region.

It doesn't want to go to war in the Middle East.

It pursued a nuclear deal with Iran.

It wants to focus on Ukraine.

So that -- so, to that extent, this is good for the United States.

But, on the other hand, President Biden has been on the record in Saudi Arabia saying that the most important way to think about the Middle East is a very close Arab-Israeli alliance against Iran, in other words, everybody together against Iran.

And this deal, also the fact that he's moved so quickly, really puts the question that - - that strategy, so -- and, for the Israelis, it's definitely a net loss.

Israel wanted the Middle East to focus on Iran and forget about the Palestinians.

That's the way the Trump administration saw it.

We're now seeing things reverse.

In other words, the Arabs are not thinking about Iran, and the Palestinian issue is heating up.

So, in -- to that extent, basically, the way Israel and the United States approached Iran and the Middle East is no longer at play.

AMNA NAWAZ: Vali, what about the fact that this meeting took place in Beijing, and it was mediated by China?

What does that say to you about China's influence in the region, in particular, a region where the U.S. seems to be losing influence?

VALI NASR: I think it says a lot.

First of all, the Chinese do have a vested economic and strategic interest in both Iran and Saudi Arabia.

So they approach the Middle East with a view that they don't want these two sides to fight.

It benefits China, if they make peace.

It also shows that Saudi Arabia and Iran both trust China and particularly China's president, and that he has been able to deliver, not only get an initial handshake, but keep getting handshakes and keep the momentum going forward.

It has broad implications for the United States, because it largely says that America's closest allies in the Gulf, Saudi Arabia, and then potentially UAE, et cetera, are now moving much more into an orbit of nonalignment and closer proximity to China, which then will have implications for a variety of other issues that the United States has with those countries.

AMNA NAWAZ: Vali, in the 30 seconds or so I have left, while I have you, because you know the region so well, I just want to get your assessment of what we're seeing in the way of escalating tensions and conflict between Israeli forces and Palestinian militants.

How do you see it?

VALI NASR: I think it's very dangerous.

We're seeing -- we're seeing the Palestinian issue come back with a vengeance.

As I said, President Trump assumed that the Palestinian issue was dead.

The Israelis thought the Palestinian issue is dead, it's all going to be about Iran.

And now, all of a sudden, the Palestinian issue is making a big comeback.

And that's going to have a big impact on the Arab street and on the mentality of Arab leaders.

And it's almost like we're back to the future.

We're back to the time when the Palestinian issue was very decisive in Middle East affairs.

AMNA NAWAZ: That is Vali Nasr, formerly of the State Department, now at the Johns Hopkins University School of Advanced International Studies, joining us tonight.

Vali, thank you.

Always good to see you.