"This is not the time to fall back," said al-Jaafari.
Mr. Bush rejected the idea of setting a timetable for the withdrawal of U.S. forces from Iraq.
"Why would you say to the enemy here's a timetable, just go ahead and wait us out? That doesn't make any sense to have a timetable. If you give a timetable you're conceding too much to the enemy," Mr. Bush said at a joint White House news conference.
The two leaders fielded questions hours after aattacked a U.S. military convoy in Fallujah, killing five U.S. Marines and a sailor.
Mr. Bush conceded that it bothers Americans to see scenes of carnage on television.
"There's no question there's an enemy that still wants to shake our will and get us to leave," he said. "They try to kill and they do kill innocent Iraqi people, women and children 'cause they know that the carnage that they reap will be on TV and they know that it bothers people to see death."
"It does. It bothers me. It bothers American citizens. It bothers Iraqis," Mr. Bush said.
Mr. Bush said he would stay the course in Iraq despite public opinion polls showing dwindling support for his policies. He indicated his awareness of his domestic critics when a reporter began asking a question about whether he was concerned about a "slump" in his support.
"Quagmire?" the president asked, employing a word that some Democrats in Congress have begun to use to describe the military presence in Iraq one year after the transfer of sovereignty.
His visitor, al-Jaafair, seemed to recognize the domestic pressure on the president.
"You have given us more than money," he told Mr. Bush. "You have given us your sons and your daughters ... this is more precious than any other support we have received."
More than 1,700 American troops have died in Iraq, the majority of them since the end of hostilities aimed at toppling the regime of Saddam Hussein. There have been 479 car bombs in Iraq since the handover of sovereignty on June 28, 2004, according to an Associated Press count.