"Jordan fully backs reconciliation efforts in Iraq, whose stability and security is key to regional security," a palace statement quoted the king as telling Allawi.
The king said, "It's important to form an Iraqi government that reflects the aspirations of the Iraqi people, ensures a better future and safeguards national unity."
Allawi's Iraqiya political bloc earned 91 seats in Iraq's March 7 elections, two seats ahead of the State of Law alliance of incumbent Iraqi Premier Nuri Al-Maliki, in the battle for control of the 325-member Council of Representatives.
The two parties have been locked in a battle for control of the council, shuffling through potential coalitions that could win them power.
Allawi, a moderate Shiite whose political grouping attracted support from Sunnis, was in Jordan as part of a regional tour.
On Oct. 17, Al-Maliki visited the kingdom for talks with the king.
Meanwhile, a bomb blast Wednesday near a Sunni religious organization killed two security guards, police and hospital officials said.
The roadside bomb exploded at a checkpoint about 500 meters from the main gate of the Sunni Endowment, a government-supported institution that oversees mosques, schools and cemeteries. Three guards and two others were injured.
A worker at Baghdad's Al-Numan Hospital confirmed the casualties.
Elsewhere in Baghdad, a bomb hidden in a pickup truck exploded, killing the driver and injuring three passers-by.
An official at Yarmouk Hospital confirmed the death.
The motives for the attacks were not known.
All officials spoke on condition of anonymity because they were not authorized to brief the media.
