The president made his appeal just hours after rockets fired from Hamas-controlled Gaza landed in a southern Israeli border town, a fresh reminder of the severe security risks and tensions that have stymied peace efforts for decades.

Obama, on his second day in the Middle East, shuttled between Jerusalem and Ramallah, reaching out to the public as well as political leaders. He offered no new policies or plans for reopening peace talks but urged both sides to "think anew" about the intractable conflict and break out of the "formulas and habits that have blocked progress for so long."

"Peace is possible," Obama declared during an impassioned speech to young people in Jerusalem. "I'm not saying it's guaranteed. I can't even say that it is more likely than not. But it is possible."

The deep disputes dividing the Israelis and Palestinians have remained much the same over the years, and include deciding the status of Jerusalem, defining borders and resolving refugee issues. Palestinians have been particularly incensed over Israeli settlements in disputed territories, and the Israelis' continued construction has also drawn the condemnation of the United States and other nations.

Further settlement activity is "counterproductive to the cause of peace," Obama said. But in a notable shift, he did not repeat his administration's previous demands that Israel halt construction. Instead, he urged the Palestinians to stop using the disagreement as an "excuse" to avoid talks.

"If the expectation is that we can only have direct negotiations when everything is settled ahead of time, then there is no point for negotiations," Obama said during a joint news conference with Palestinian Authority President Mahmoud Abbas in Ramallah. "I think it is important to work through this process even if there are irritants on both sides."

Abbas said Palestinians remain committed to seeking peace with Israelis, but he made clear that settlement construction had made his people distrustful of Israel's intentions.

"This is very dangerous that people and the new generation reaches the conviction that it's no more possible to believe in the two-state solution," he said.

Obama has sided with the Palestinians on the settlement issue during his first four years in office. However, when Israel reluctantly declared a 10-month moratorium on construction, the Palestinians balked at returning to negotiations until shortly before the suspension expired and talks foundered shortly thereafter.

The Palestinians want a state in the West Bank, Gaza and East Jerusalem -- territories Israel captured in the 1967 war -- but indicate they are ready for minor adjustments to accommodate some settlements closest to Israel. Since 1967, Israel has built dozens of settlements in the West Bank and East Jerusalem that are now home to 560,000 Israelis -- an increase of 60,000 since Obama became president four years ago.

Upon his return to Israel, the president told Israelis that in the search for peace they have "true partners" in Abbas and Salam Fayyad, the Palestinian prime minister.

Obama is spending the majority of his four-day Mideast trip in Israel, where the politicians and public have been skeptical of his commitment to their security. The president has sought to calm their concerns throughout his visit, reminding an audience of Israeli university students Thursday that the U.S. is their country's best friend and most important ally.

"You are not alone," Obama declared as the crowd erupted in thunderous applause.

Still, he nudged Israel to take steps to reverse an "undertow" of international isolation that is worsened by its failure to make peace with the Palestinians. In a region roiled by political unrest, Obama said the days when the Israelis can seek protection from a handful of autocratic leaders in other nations are over, and he urged them to seek common ground with the Arab people, not just their governments.

Hours before Obama arrived in the West Bank, militants in the Gaza Strip launched at least two rockets at the southern Israeli town of Sderot, causing damage but no injuries, according to Israeli officials. As a presidential candidate in 2008, Obama visited the border town, which is frequently targeted in rocket attacks.

A small, murky, al-Qaida-inspired group calling itself the Mujahideen Shura Council in the Environs of Jerusalem claimed responsibility for the rocket fire. In a statement emailed to The Associated Press, it said it was sending a message to "Osama's soldiers" to protest the visit by "the Roman dog Obama" and to continue its campaign of holy war.

Over the past decade, Gaza militants have fired thousands of rockets and mortar shells at Israel, prompting Israel, with considerable U.S. assistance, to develop its Iron Dome missile defense system, which it credits with intercepting many rockets.

The president closed his five-hour trip to the West Bank with a visit to a U.S. government-funded youth center, where he cheered a performance by a dance troupe and held a private roundtable discussion with a small group of young Palestinian men. He recalled the conversation later in his Jerusalem speech, saying that if "any Israeli parent sat down with those kids, they'd say, 'I want these kids to succeed; I want them to prosper.' I believe that's what Israeli parents would want for these kids if they had a chance to listen to them and talk to them."

While Obama was welcomed warmly in Israel, where U.S. and Israeli flags dotted the roadsides, Palestinians showed little excitement over Obama's shorter stop in the West Bank. Protesters defaced and burned posters of Obama in an expression of dissatisfaction with U.S. policy in the region. Several dozen demonstrators also gathered in downtown Ramallah during Obama's meetings, protesting what is perceived in the Palestinian territories to be a strong U.S. bias in favor of Israel.

The president opened the second day of his trip at Jerusalem's Israel Museum, a stop aimed at highlighting both the Jewish people's ancient connection to the land that is now Israel and the small nation's thriving modern economy.

The president and Israeli Prime Minister Benjamin Netanyahu viewed the Dead Sea Scrolls, the ancient Hebrew texts. It was a symbolic visit for Obama, who has battled against a perception in Israel that he sees the Holocaust, not historical ties to the region, as the rationale for the existence of the Jewish state. The president has repeatedly sought to correct that impression.

As he viewed the ancient scrolls displayed in a dimly lit room, Obama marveled at how the Hebrew language had changed so little that Netanyahu could read some of the writings. The two then toured a technology exhibit at the museum featuring several modern Israeli inventions, including an electric vehicle battery, a technology Obama has promoted in the U.S.

Obama was awarded Israel's Medal of Distinction Thursday night during a lavish dinner. He is the first sitting U.S. president to receive Israel's highest civilian honor.

Associated Press writers Matthew Lee, Ian Deitch and Josef Federman in Jerusalem, and Karin Laub and Mohammed Daraghmeh in Ramallah contributed to this report.