AMMAN, Jordan - President Bush pledged Thursday that US troops will remain in Iraq to strengthen the authority of embattled Prime Minister Nouri al-Maliki and said the two agreed to speed a turnover of security responsibility to Iraqi forces.

"One of his frustrations with me is that he believes that we've been slow about giving him the tools necessary to protect the Iraqi people," Bush said. "Today we had a meeting that will accelerate the capacity for the prime minister to do the hard work necessary to help stop this violence."

The two also agreed in high-stakes talks here Thursday that Iraq should not be partitioned into separate, semiautonomous zones.

"The prime minister made clear that splitting his country into parts, as some have suggested, is not what the Iraqi people want, and that any partition of Iraq would only lead to an increase in sectarian violence," Bush said after he and the Iraqi prime minister met for nearly two and a half hours.

While Bush continued to reject drawing Iran into helping Iraq in its struggle for peace, Al-Maliki left the door open for countries like Iran and Syria to play a part.

"We are ready to cooperate with everybody who believes that the need to cooperate with the national unity government, especially our neighbors," al-Maliki said.

He said that "Iraq is for Iraqis and its borders will be sound."

Bush and al-Maliki had been set to start meeting on Wednesday, but that opening session was canceled following disclosure of US doubts about the Iraqi leader's capabilities and a Baghdad protest of his attendance.

But any tension over that stunning turn of events was not apparent when the leaders appeared together before reporters. "He's a strong leader who wants a free and democratic Iraq to succeed," Bush said.

The president acknowledged the pressure at home for the beginning of US troop withdrawals but he said, "We'll be in Iraq until the job is complete, at the request of a sovereign government elected by the people."

He said the United States - which now has about 140,000 troops in Iraq - will stay "to get the job done so long as the government wants us there."

Bush said he wanted to begin troop withdrawals "as soon as possible. But I'm a realist because I understand how tough it is inside of Iraq."