"That's not something that would make it likely that we would remain engaged because, one, the American people would have no interest in doing that, and, as he put it, neither would he nor the president," the official said, speaking on condition of anonymity in order to discuss the confidential talks.

"There also wasn't any appetite to put Humpty Dumpty back together again if, by the action of people in Iraq, it fell apart," the official added.

Biden expressed particular concern that Arab-Kurdish tensions in the north might erupt into violence, according to a close al-Maliki aide.

Al-Maliki's adviser Yassin Majid said the prime minister told Biden that national reconciliation has always been on his government's agenda and that he had saved the country from plunging into civil war.

But he also said al-Maliki had no plans to embrace remnants of Saddam's ousted Baath Party, calling that "a red line," and he warned some groups want to exploit reconciliation for partisan gains.

Biden's visit and his new position overseeing the U.S. administration's Iraq policy reflect growing concern about a recent rise in violence after a series of bombings that killed scores of people.

A roadside bomb exploded on a street in Youssifiyah, south of Baghdad, on Saturday, killing one civilian and wounding five others, police said.

Al-Maliki, a Shiite, has been criticized for failing to take advantage of security gains to make progress in overcoming disputes between Shiites, Sunnis, Kurds and other groups as divisions deepen before Jan. 30 general elections.

Violence remains at low levels in Iraq compared with previous years, but U.S. and Iraqi officials have warned of more attacks after the city withdrawal deadline and in the run-up to the elections.

At least 447 Iraqi civilians were killed in June, double the toll from the previous month, according to an Associated Press tally.

Al-Maliki has called the U.S. withdrawal from cities a "great victory" and declared June 30 National Sovereignty Day.

On Friday, he expressed gratitude for the U.S. support.

"I have seen very clearly the keen determination from the vice president and his administration to support Iraq ... and a great readiness to give us a lending hand and support anywhere we ask," he said.