Mr. Obama met with Mr. Abbas and the prime minister of the Palestinian Authority, Salam Fayyad, for one hour  15 minutes longer than scheduled  at the Muqata, the Palestinian president’s compound. Mr. Obama and Mr. Abbas sat down with a Palestinian flag between them and photographs of the late Palestinian leader Yasir Arafat and of Mr. Abbas himself on the wall behind them.

Saeb Erekat, a senior aide to Mr. Abbas and a senior Palestinian negotiator, said in an interview after the meeting that Mr. Obama seemed to be committed to helping both sides achieve a peace accord and was supportive of pursuing a two-state solution.

“My impression is that he is focused,” Mr. Erekat said. “He believes it is in the American national interest and that time is of the essence. He said he won’t waste any time, and that he’ll be a constructive partner.”

Image Mr. Obama went to the West Bank city of Ramallah to have talks with the Palestinian president, Mahmoud Abbas. Credit... Omar Rashid/European Pressphoto Agency

Yet even as Mr. Obama treaded carefully through the perilous path of the Middle East peace process, he was left to defend a proposal he made a year ago to negotiate with Iran. He said he would “take no options off the table” to persuade that country’s leaders not to develop nuclear weapons.

“My whole goal,” he said, “in terms of having tough, serious direct diplomacy is not because I’m naïve about the nature of any of these regimes. I’m not. It is because if we show ourselves willing to talk and to offer carrots and sticks in order to deal with these pressing problems  and if Iran then rejects any overtures of that sort  it puts us in a stronger position to mobilize the international community to ratchet up pressure on Iran.”

Senator John McCain, the presumptive Republican nominee, suggested that Mr. Obama had reversed a position he took a year ago when he said he was willing to meet with Iranian leaders without preconditions. For months, Mr. Obama has struggled to explain consistently about whether  and how  he would sit down with rogue leaders.