ISTANBUL, Turkey — President Obama continued to use his bully pulpit on Tuesday to call for Israelis and Palestinians to make the compromises necessary to reach a Middle East peace accord.

During a question-and-answer session with university students here, Mr. Obama said that he still believes that “peace in the Middle East is possible. I think it will be based on two states side by side,” he said.

“What we need,” Mr. Obama said, “is political will and courage on the part of the leadership.”

His comments come a day after he publicly repudiated statements from Israel’s hawkish new foreign minister, Avigdor Lieberman, that agreements reached at an American-sponsored peace conference in Annapolis, Md., in 2007 have “no validity.”

Speaking before the Turkish parliament on Monday, Mr. Obama said that Palestinian statehood was “a goal that the parties agreed to in the roadmap and at Annapolis. That is a goal that I will actively pursue as president.”

The road map refers to a 2003 outline of steps toward a peace agreement.

Mr. Obama, nearing the end of his maiden overseas trip, made an effort to connect with the young people assembled before him in Istanbul’s Tophane-I-Amire Hall, a centuries-old exhibition hall. He took questions from them about climate change, Turkey’s entry into the European Union and whether he was, deep down, more like President Bush than he admitted. (To that, Mr. Obama replied that changing United States policy was more like turning a tanker ship, and would take time.)

He often reverted to his favorite rhetorical devices — straw men — to make his points to the students. For instance, he said that “some people say that I’m being too idealistic” and ask him why he’s reaching out to Iranians, saying that trying to use diplomacy to stop Iran from getting a nuclear bomb is “too hard.”

“My attitude is all these things are hard,” Mr. Obama said. He added that he believed he still had to try.

“I am personally committed to a new chapter in American engagement,” Mr. Obama told the students, who sat in a tight circle around him. “We can’t afford to talk past one another and focus only on our differences, or to let the walls of mistrust go up around us.”

Mr. Obama spent the morning meeting with religious leaders, and then went on a tour of Hagia Sophia, once the biggest church in Christendom and now a museum, and the famed 17th-century Blue Mosque.

His plane departed Istanbul at 2:30 p.m. local time.

On Monday, setting out his perspective on America’s relationship with the Islamic world, Mr. Obama told the Turkish Parliament that: “America’s relationship with the Muslim community, the Muslim world, cannot and will not just be based upon opposition to terrorism,” he said. “We seek broader engagement based upon mutual interest and mutual respect.”

Showing more self-confidence each day on his trip, Mr. Obama, in addressing a majority Muslim country for the first time, appeared to have prepared carefully for one particular line in his wide-ranging speech.

“The United States has been enriched by Muslim-Americans,” he said. “Many other Americans have Muslims in their family, or have lived in a Muslim-majority country.

“I know,” he said, “because I am one of them.”

And then he paused. Throughout his speech, he had moved swiftly from passage to passage, but this time, he waited for the interpreter to catch up. After about five seconds, the applause came.

The line was a bold one for Mr. Obama, who has been falsely described as a Muslim. The claim persists on some right-wing Web sites, which may try to interpret his remarks as proof of that view.

But Mr. Obama, who spent part of his childhood in Indonesia, is calculating that the benefits of demonstrating to the Muslim world that Americans are not antagonistic toward it outweigh the potential political fallout back home. His calculus may also reflect an increased belief that he has enough political capital that he can spend some of it in pursuit of strengthening ties between Muslim nations and the West.

Introduced as “Barack Hussein Obama,” the president told the assembly that he planned to push for a two-state solution in the Middle East, despite the view of many foreign policy experts that such a goal will be even more difficult to reach because of the makeup of the new Israeli government under Prime Minister Benjamin Netanyahu, not to mention the fractured state of internal Palestinian politics.

Turkey is crucial to American interests on many fronts. It borders Iraq and Iran; it has deep influence in Afghanistan; and it is helping efforts to forge a peace deal between Israel and Syria.

In choosing Turkey as an example of the type of relationship that can be struck between the United States and an Islamic population, Mr. Obama also seemed to be pushing for more acceptance of the separation of religion and the state. Turkey is a secular Muslim democracy that has recently seemed at war with itself over its own religious identity. Its prime minister, Recep Tayyip Erdogan, has roots in political Islam, a worry to secular Turks.

On Monday morning, Mr. Obama went to pay his respects at the Ankara mausoleum of Mustafa Kemal Ataturk, a secularist who established modern Turkey, and the president wrote at some length in a guest book at Ataturk’s shrine.

“It is also clear that the greatest monument to Ataturk’s life is not something that can be cast in stone and marble,” Mr. Obama said during his speech. “His greatest legacy is Turkey’s strong, vibrant secular democracy, and that is the work that this assembly carries on today.”

Mr. Obama also threw his weight solidly behind Turkey’s accession to the European Union, an issue that has split Europe, with France and Germany lobbying against Turkey’s entry.

“Let me be clear: the United States strongly supports Turkey’s bid to become a member of the European Union,” he said. “We speak not as members of the E.U., but as close friends of both Turkey and Europe.”

The president also waded into the fraught issue of Turkey’s relations with Armenia, and the genocide of more than a million Ottoman Armenians beginning in 1915. Turkey acknowledges the killings but says they did not amount to a systematic genocide, and it has vehemently opposed the introduction of a bill in the United States Congress that would define it that way.

As a senator, Mr. Obama voiced support for the legislation, but during a news conference with President Abdullah Gul before the Parliament speech, he did not use the word genocide and said Turkey and Armenia had made progress in talks.

Armenian-Americans were quick to voice their ire.

“In his remarks today in Ankara, President Obama missed a valuable opportunity to honor his public pledge to recognize the Armenian genocide,” Aram Hamparian, executive director of the Armenian National Committee of America, said in a statement.

Mr. Obama’s remarks, he said, fell “far short of the clear promise he made as a candidate that he would, as president, fully and unequivocally recognize this crime against humanity.”

During the Parliament speech, Mr. Obama did speak of the Armenia issue, saying, “History is often tragic, but unresolved, it can be a heavy weight.”

He said that the United States “still struggles with the legacies of slavery and segregation, the past treatment of Native Americans.”