JEFFREY BROWN: President Obama called on young Israelis to see the world through Palestinian eyes and challenged Israeli and Palestinian leaders to abandon -- quote -- "formulas and habits that have blocked peace."
But even amid his visit, the old threats and realities of violence were present.
Margaret Warner reports from Jerusalem.
MARGARET WARNER: The second day of the president's trip to Israel and the West Bank was met with rocket fire from one place Mr. Obama won't go, Hamas-controlled Gaza.
Two landed in Sderot, Israel, a clear breach of the cease-fire the Islamist Hamas faction and Israel struck late last year. There were no injuries. A little-known militant group claimed responsibility, saying it wanted to show that Israel could not protect its airspace during Mr. Obama's visit.
The Israeli mayor of Sderot said there was another message from militants to President Obama.
Mayor David Buskila, Sderot: The message is, why you go to Ramallah? We are the owners of this region. You can arrive to Gaza and talk with us. Why do you go to talk with Abu Mazen in Ramallah?
MARGARET WARNER: Abu Mazen is Palestinian President Mahmoud Abbas, who greeted Mr. Obama in Ramallah on the West Bank at midday. A small band of protesters in the city center was kept well away. Just outside the city, there were minor clashes with Israeli troops.
The two leaders held talks on one priority of president's four-day visit to the Middle East, reinvigorating peace talks between Israelis and Palestinians. But contrary to the apparent and unusual chumminess with Prime Minister Netanyahu yesterday, Mr. Obama and Abbas displayed an understated, businesslike tone in their brief press conference.
The president denounced the morning's rocket attack and the group that rules in Gaza.
PRESIDENT BARACK OBAMA: Hamas cares more about enforcing its own rigid dogmas than allowing Palestinians to live freely, and because too often it focuses on tearing Israel down rather than building Palestine up.
MARGARET WARNER: On the issue at hand, the president did say his administration was committed to give the moribund peace process another try, and he urged the Palestinians to do the same.
But Israel's continued expansion of Jewish settlements on the West Bank has been a stumbling block to reviving peace negotiations. The Palestinians have made halting Israeli construction a condition for restarting talks.
Mr. Obama initially joined that call in 2009, but hasn't since.
Today, Abbas seemed to reaffirm that insistence, though he didn't use the word condition.
PRESIDENT MAHMOUD ABBAS, Palestinian Authority: It is the duty of the Israeli government to at least halt the activity, so that we can speak of issues. And when we define our borders and their borders together, each side will know its territory in which it can do whatever it pleases. So the issue of settlements is clear.
MARGARET WARNER: But the president said, while settlement activity wasn't constructive for peace, setting preconditions for talks was counterproductive too.
PRESIDENT OBAMA: We do not consider continued settlement activity to be constructive, to be appropriate, to be something that can advance the cause of peace.
If the only way to even begin the conversations is that we get everything right at the outset, then we're never going to get to the broader issue, which is how you actually structure a state of Palestine that is sovereign, contiguous, and provide the Palestinian people dignity.
MARGARET WARNER: The president also met with young Palestinians, many of whom have lost faith in any resolution to the decades-old conflict.
Back in Jerusalem, before thousands of mostly young Israelis, the president gave the featured address of his Mideast tour. While reiterating America's unwavering support of Israel, he also called on them to identify with their young Palestinian counterparts.
PRESIDENT OBAMA: And put yourself in their shoes. Look at the world through their eyes. It is not fair that a Palestinian child cannot grow up in a state of their own.
It is not right to prevent Palestinians from farming their lands, or restricting a student's ability to move around the West Bank, or displace Palestinian families from their homes.
Neither occupation nor expulsion is the answer.
Just as Israelis built a state in their homeland, Palestinians have a right to be a free people in their own land.
MARGARET WARNER: In a speech shot through with adrenaline from the president and the crowd, Mr. Obama echoed some of the themes that helped get him elected in 2008, that citizens can and should compel their leaders to act.
PRESIDENT OBAMA: And let me say this as a politician. I can promise you this. Political leaders will never take risks if the people do not push them to take some risks. You must create the change that you want to see.
MARGARET WARNER: The evening closed with a state dinner in Israel. Tomorrow, the president leaves for Jordan.