The king spoke after meeting Muqtada al-Sadr, an Iraqi Shia cleric who is on a regional tour to promote better relations with neighbouring countries.
Abdullah said in a statement issued by the Royal Palace: "It's our duty to protect the future of Iraq and we are always ready to put our best efforts forward to make this a successful outcome."
He affirmed Jordan's desire for a unified Iraq and the guarantee of a better future so that the country could regain its vital role in the region, the statement said.
Abdullah added that Iraq's success was as of much interest to Jordan as to Iraq.
Government officials were not immediately available to comment further on the meeting.
Al-Sadr said: "I came to Jordan to meet my family and my brothers here and to consolidate co-operation between us."
Al-Sadr also expressed appreciation for Abdullah's efforts in the Arab and international arenas in clarifying the true image of Islam and its prophet, especially during his trip to Washington earlier this month.
Abdullah, who has close ties with the United States, met George Bush, the US president, and other top officials on his trip, and addressed the National Prayer Breakfast, an annual gathering of politicians and dignitaries.
Al-Sadr, who once fiercely battled US troops, has climbed Iraq's political ladder recently but maintains his anti-American stand.
In an Aljazeera interview on Saturday, al-Sadr accused Washington of trying to drive a wedge between Iraq and its neighbours and to hinder the development of the country's security forces to justify the US presence.
Earlier that day, al-Sadr said the withdrawal of US and other foreign forces "should be the priority of the future Iraqi government".
In the same interview, al-Sadr rejected the Iraqi constitution backed by his partners in the biggest parliament bloc.
"If there is a democratic government in Iraq, nobody has the right to call for the establishment of federalism anywhere in Iraq"
He said: "I reject this constitution which calls for sectarianism and there is nothing good in this constitution at all."
He criticised federalism in the constitution, which is rejected by Iraq's Sunni Arabs, who fear it will give Kurds and Shias too much power and control over Iraq's oil resources.
He said: "If there is a democratic government in Iraq, nobody has the right to call for the establishment of federalism anywhere in Iraq whether it is the south, north, middle or any other part of Iraq."
Meanwhile, Mahmoud Othman, a prominent Kurdish politician, said talks between Kurdish and Shia leaders on forming a new government are "not going well" because of major policy differences.
That could delay formation of a new government and any drawdown of US forces.
Othman, a member of the Kurdish negotiating committee, said talks were facing problems over several issues, including a proposed oversight council and the system for taking government decisions.
Othman said: "If the position of the Shia alliance is final, then things will be more complicated and the formation of the government might face delays."
Under the new constitution, formation of the new government should be complete by mid-May, although some US officials believe the process could take longer.