"As a key component of the Iraqi social fabric, the Iraqi Sunni community must be included as partners in building Iraq's future," said the king, a top US ally in the Mideast.
Along with other Sunni Arab states like Egypt and Saudi Arabia, Jordan is increasingly concerned by the growing Shia influence in Iraq, Syria and Lebanon.
Plea for Palestine
Abdullah also "called on the United States to actively push for a revival of Palestinian-Israeli peace negotiations," the statement from his office said.
"Bush's strategy has failed totally in Iraq and USA has already lost the war. The new plan will not work; it will only bring more deaths and make things in Iraq worst..."
Dimos, Hania-Crete, Greece
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He told Rice that this "would lead to the establishment of a viable, independent Palestinian state that would fulfill Palestinian aspirations for freedom, independence and security."
However Abdullah also warned that "without tangible, specific steps to activate the implementation of the road map in the near future, the cycle of violence will widen."
The US-backed 'road map' peace plan calls for the creation of an independent Palestinian state.
The Jordanian monarch also called on the solution to the Israeli-Palestinian conflict to be based on international legality and the Arab Peace Initiative.
This initiative, unveiled at an Arab summit in Lebanon in 2002, calls for Israel to withdraw from all territory occupied since the 1967 Mideast war in return for full recognition by Arab countries.
Rice arrived in Jordan earlier Sunday from the West Bank, where Mahmoud Abbas, the Palestinian president, told her that he opposed the establishment of a provisional Palestinian state in temporary borders, a key part of the road map.