Abdullah said the terror plots aims to elicit an Israeli response in a bid to distract attention from Damascus' problems in Lebanon.
The king said he already warned Prime Minister Ariel Sharon about the plan and informed him of Hizbullah complicity in the next terror attack, should it occur.
King satisfied with Sharm summit
Palestinian Authority Chairman Mahmoud Abbas is committed to the fight against terror, even though he is unable to disarm terror organizations at this time, Abdullah said at the meeting.
He added that he is satisfied with the recent Sharm al-Sheikh summit's outcome and the steps that have followed.
Behind the scenes there are other Arab countries, which he declined to name, that are also interested in promoting their relations with Israel, Abdullah said.
During his visit to Washington, Abdullah also met with Secretary of State Condoleezza Rice.
A visit to Israel?
Meanwhile, Abdullah is planning to visit Israel and the Palestinain Authority in the coming weeks, Jordanian Prime Minister Faisal al-Fayez told a delegation of Arab-Israeli Knesset members visiting Amman in February.
Sources in Jerusalem confirmed there have been talks to coordinate a visit with the Palestinian Authority, but said a date has not yet been set.
The planned trip would mark the second official visit by the Jordanian king to Israel.
In August 2000, Abdullah made a quick three-and-a-half-hour visit to Israel to attend a memorial service for late Prime Mister Yitzhak Rabin.