"The truth is in some of these conflicts the United States can't impose solutions unless the participants in these conflicts are willing to break out of old patterns of antagonism," Obama told a news conference on Tuesday.
The US president recently acknowledged he had underestimated the obstacles to a renewed peace process, and some critics have called his approach naive.
"The Israeli people, through their government, and the Palestinian people, through the Palestinian Authority, as well as other Arab states may say to themselves: 'We are not prepared to resolve these issues no matter how much pressure the United States brings to bear'," Obama said.
But he said that the US would press on, "constantly present, constantly engaged".
"It's going to take time, and progress will be halting," Obama said. "And there will be frustrations."
Despite shuttle diplomacy and unusual pressure on Israel, the Obama administration has been unable to reach even the modest goal of reviving talks between Israel and the Palestinians.
Last week, Binyamin Netanyahu, the Israeli prime minister, acknowledged that his government had yet to resolve its differences with the US over Israeli construction in occupied East Jerusalem – a major sticking point that torpedoed indirect talks before they could even start.
Netanyahu said both countries were still working to find a solution but staunchly defended his government's continued settlement building in Jerusalem as a "long-standing Israeli policy".
"There are things we agree on, things we don't agree on, things we are closing the gap on," Netanyahu said.
"We are making an effort.''
The breakdown in US-Israeli ties began after Israel announced plans to build 1,600 new housing units in occupied East Jerusalem during a visit by Joe Biden, the US vice-president, drawing sharp condemnation from Washington.
Palestinians want East Jerusalem as the capital of an independent Palestinian state in any two-state solution to the situation and have demanded that all settlement acticity is halted before talks can resume.
Negotiations between Israel and the West Bank-based Palestinian Authority have been stalled since Israeli forces began a 22-day military offensive in the Gaza Strip, controlled by the rival Hamas movement, more than a year ago.