BAGHDAD – Monday's visit had not been announced. An earlier trip set for July was canceled because Jordanian officials did not want any advance publicity.
Iraqi officials, speaking on condition of anonymity because of Jordanian sensitivities, said the visit lasted only four hours and the king left ahead of the announcement.
U.S. officials had been urging Abdullah to visit Iraq to bolster ties between the two countries. Jordanian officials have been concerned about the rise of a pro-Iranian Shiite government in Iraq and the loss of discounted oil, which Saddam once provided.
Al-Maliki visited Jordan in June for the first time in nearly two years, and since then, the two nations appear willing to put their differences behind them.
The Iraqi prime minister at the time agreed to renew oil supplies to his cash-strapped neighbor for the next three years at discounted prices.
Jordan agreed to ease restrictions on the entry of Iraqi students and those transiting to a third country.
Jordan has also named an ambassador to Iraq, joining other Arab countries that have agreed to upgrade their relations as the Iraqi government becomes more stable and security has improved — despite sporadic attacks and ongoing military operations.
Also Monday, the government said it has halted military operations in Diyala province for a week to give insurgents time to surrender, even as deadly bombings struck the area northeast of Baghdad.
In the most dramatic attack, a female suicide bomber struck a market checkpoint in the provincial capital of Baqouba, killing at least one policeman and wounding 14 other people, including nine officers, officials said. They spoke on condition of anonymity because they were not authorized to talk to media.
The woman detonated explosives hidden under her traditional Islamic black robe as she approached the checkpoint manned by Iraqi police at the central market, witnesses said.
The blast sent black smoke billowing into the sky. Iraqi security forces began shooting into the air to clear the area while shoppers and shop owners began shouting and running from the site.
Another bomb exploded in the Wijaihiyah area, about 12 miles east of Baqouba, killing two women and wounding four people, including a child, according to the Diyala security operations center.
Sporadic attacks have continued in Diyala — including several carried out by women — despite a new U.S.-Iraqi military operation launched last month in the latest government crackdown against suspected insurgent hideouts in the area.
The Iraqi Defense Ministry said al-Maliki has ordered the Diyala military operations to be suspended for a week starting Monday "to give gunmen a chance to surrender."
The prime minister's office has announced an amnesty offer and unspecified monetary rewards for those who hand over "heavy and medium weapons, roadside bombs, rifles or any other kind of explosives," according to a statement.
Al-Maliki has made amnesty offers during similar operations against Sunni and Shiite extremists in Baghdad's Sadr City district, Mosul and the southern cities of Basra and Amarah, but they have had limited effect.
Violence also struck the capital Monday.
A bomb stuck under a car exploded in eastern Baghdad, killing the driver and wounding two other people, police said.
The U.S. military, meanwhile, confirmed that the suicide bomber who killed a U.S. soldier and at least four Iraqis on Sunday in an attack north of the capital also was a woman.
An Iraqi police official, who spoke on condition of anonymity because of security concerns, said 23 Iraqis were killed, including six members of a U.S.-allied Sunni group, three Iraqi security forces and 14 civilians. The conflicting casualty tolls couldn't be reconciled.
The female suicide bomber struck as U.S. and Iraqi troops were responding to a roadside bombing that wounded an Iraqi in Tarmiyah, 30 miles north of Baghdad, the U.S. military said.
Lt. Col. Steve Stover, a spokesman for U.S. forces in Baghdad, said a wanted al-Qaida in Iraq militant was arrested near the scene.
The U.S. military has warned that Sunni insurgents are increasingly recruiting and using women to carry out bombings because they are more easily able to hide explosives under their robes and avoid being searched at checkpoints.
In response, the U.S. has stepped up efforts to recruit and train women for Iraq's police force and enlist them to join Sunnis fighting al-Qaida.
U.S. military figures show some 30 female suicide bombings this year, compared with eight in 2007.