"There was an agreement that the US president should exert pressure to fulfill his promises concerning the establishing of an independent Palestinian state," Jamal Shobaki told AFP following the meeting between the two leaders.
"There is a feeling that the US administration is still not willing to take a decisive position towards the Israeli government," to push for an agreement over a Palestinian state, he added.
Abbas also briefed the monarch on his recent talks in Washington and Moscow, Shobaki said, adding that the Palestinian leader left for Amman after the talks.
The White House announced on Monday that Bush will visit Israel, Saudi Arabia and Egypt between May 13 and 18.
Bush, who is seeking a Middle East peace deal by year’s end, will meet Abbas in Egypt.
Abbas, who met Bush at the White House last week, has warned of an "extremely difficult impasse" if a peace deal is not reached with Israel before Bush leaves office in January.
The Palestinian leader earlier visited Moscow, where he discussed a Middle East peace conference which Russia is proposing to host with outgoing President Vladimir Putin.
