Obama vowed an "aggressive" mediation effort, ahead of his visit to Saudi Arabia and Egypt next week, while Abbas pledged to live up to all previous peace agreements and warned "time is of the essence" for a two-state solution.
The US president recalled that last week he had been "very clear" with Netanyahu about the need to "stop settlements" and again stated his desire to see a two-state solution to the Israeli-Palestinian conflict.
He was asked by a reporter if he would strong-arm Israel if it did not back down in its refusal to support a Palestinian state.
"I think it's important not to assume the worst, but to assume the best," said Obama, who rejected an opportunity to set a date for the establishment of a "viable, potential" Palestinian state.
"I want to see progress made, and we will work very aggressively to achieve it. I don't want to put an artificial timetable," he said.
"I am confident that we can move this forward if all parties are ready to meet their obligations."
On Wednesday, Secretary of State Hillary Clinton had significantly hardened the US position on settlements, prompting a blunt dismissal from Israel.
But Obama appeared to give Netanyahu some leeway, noting the fierce pressures imposed on the Israeli leader by his hawkish right-wing coalition.
"I think that we don't have a moment to lose, but I also don't make decisions based on just a conversation that we had last week.
"Because obviously Prime Minister Netanyahu has to work through these issues in his own government, in his own coalition," said Obama.
The US president also called on Abbas to offer security improvements to Israel and to quell anti-Israel incitement in Palestinian mosques and schools.
Abbas warned that all parties should work night and day to alleviate the plight of the Palestinians and move towards statehood.
"I would like to take this opportunity to affirm to you that we are fully committed to all of our obligations under the roadmap, from the 'A' to the 'Z'," he said.
Abbas added that he had shared ideas with Obama based on the roadmap and the 2002 Saudi peace plan backed by the Arab league.
The US-backed roadmap calls for a halt to Jewish settlement activity in Palestinian territories and an end to Palestinian attacks against Israel but has made little progress since it was drafted in 2003.
Clinton had on Wednesday said Obama "wants to see a stop to settlements. Not some settlements, not outposts, not natural growth exceptions."
But Israel on Thursday dismissed the blunt US call.
"Normal life" will be allowed in settlements in the occupied West Bank, government spokesman Mark Regev said, using a euphemism for continuing construction to accommodate population growth.
He added the fate of settlements "will be determined in final status negotiations between Israel and the Palestinians and in the interim, normal life must be allowed to continue in those communities."
The Palestinian Authority has ruled out restarting peace talks with Israel unless it removes all roadblocks and freezes settlement activity.
Netanyahu told Obama last week at their first White House meeting that he was willing to "immediately" relaunch the peace talks but failed to publicly back the creation of a Palestinian state or to freeze settlement activity.
The Israeli prime minister told his cabinet Sunday he did not intend to build new settlements but that "it makes no sense to ask us not to answer to the needs of natural growth and to stop all construction," aides said.
The Abbas meeting represented Obama's latest attempt to revive the stalled Middle East peace process, which have included talks with Jordan's King Abdullah II, Netanyahu and in London with Saudi King Abdullah.
Next week, Obama will meet the Saudi King in Riyadh and deliver a long-awaited address to the Muslim world in Cairo.
But he said he would not lay out his long-awaited peace plan in the speech, which he said was designed to lay out a path for a "better" US relationship with the Islamic world.
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