Obama was expected to meet Abdullah in his private dining room, after which they were to head into the Oval Office for expanded talks with delegations from both sides, the White House said.
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 Annapolis agreement.
'Peace and security'
Two weeks ago, in an address to Turkey's parliament, Obama said "the United States strongly supports the goal of two states, Israel and Palestine, living side by side in peace and security".
A possible realisation of the two-state solution has been put in doubt with the appointment of Binyamin Netanyahu as Israel's new prime minister, who has declined to back a Palestinian state.
Commenting on reports from Israel that Netanyahu could visit the US for talks with Obama as soon as May, Gibbs said: "If the prime minister is here, the president would be anxious to sit down and talk with him, as he sat down and talked with him last year about this and other subjects that relate to our security."
But Gibbs was unable to offer any firm date on when such a meeting might take place.
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 the Amman airport.