Abbas will meet Obama in Washington next month, a senior Palestinian official said on Wednesday.
"The meeting between president Abbas and President Obama is scheduled for May 28 in Washington," Saeb Erakat, a senior Palestinian negotiator, said.
Gibbs had said that Obama invited "key partners in the effort to achieve a comprehensive peace in the Middle East to the White House in the coming weeks".
"With each of them the president will discuss ways the US can strengthen and deepen our partnerships with them, as well as the steps all parties must take to achieve peace between Israel and the Palestinians and Israel and the Arab states," Gibbs said.
'Step back from abyss'
Obama reassured Abdullah of his commitment to a two-state solution to the Middle East conflict, while calling on Israel and the Palestinians to "step back from the abyss".
"I am a strong supporter of a two-state solution. I have articulated that publicly, and I will articulate that privately," Obama said.
"And I think that there are a lot of Israelis who also believe in a two-state solution."
Obama's Middle East diplomacy has been complicated by the emergence of a coalition comprising ultranationalists led by Netanyahu, who since coming to power last month has avoided recognising the Palestinians' right to an independent state.
Obama took care not to confront Netanyahu head-on but made clear his administration hoped to coax him into accepting the principle of a two-state solution, which has been the basis of US policy for years.
"I agree that we can't talk forever, that at some point steps have to be taken so that people can see progress on the ground," he said.
"And that will be something that we will expect to take place in the coming months."
Stalled road map
In recent weeks, Obama has made it clear to Israel that he believes the path to peace lies in already agreed frameworks made in the stalled road map plan for Israeli-Palestinian peace and the agreement towards a two-state solution, which was reached at Annapolis in November 2006.
In an address to Turkey's parliament last month, Obama said "the United States strongly supports the goal of two states, Israel and Palestine, living side by side in peace and security".
Obama met both Netanyahu, who was then in opposition, and Abdullah during a visit to their two countries last year while he was still a senator.
Abdullah and Obama reportedly appeared to get along well, with Abdullah taking the unusual step of personally driving Obama to Amman airport.