BAGHDAD - U.S. Secretary of State Condoleezza Rice praised Iraq's leaders on Tuesday for passing the first in a series of critical laws aimed at reconciling warring Iraqis but said more progress was needed.

Rice held talks with Shi'ite Islamist Prime Minister Nuri al-Maliki after arriving on an unannounced visit and then met Foreign Minister Hoshiyar Zebari, President Jalal Talabani and Kurdish leader Masoud Barzani, officials said.

Washington wants Maliki's splintered government to match recent security gains with progress on political reconciliation between majority Shi'ite and minority Sunni Muslims.

Iraq's parliament voted on Saturday to let thousands of members of Saddam Hussein's Baath party return to government jobs, the first of a group of what Washington has called benchmark reconciliation laws to be passed.

"This law ... is clearly a step forward for national reconciliation, it is clearly a step forward for the process of healing the wounds of the past," Rice told a news conference.

The laws, which also include a bill on sharing oil revenues and another on provincial elections, are designed to draw Sunni Arabs, who were dominant under Saddam, back into the political process and away from Iraq's bloody insurgency.

There has been no sign of any significant progress on either the oil law or the provincial elections bill.

"Yes, there is still a lot of work to be done. I talked with the leaders today about a provincial powers law, about the need for provincial elections, we talked about the need for a hydrocarbons law," she said.

"While it has not always moved as fast as some of us sitting in Washington would like, it has certainly moved," she said of Iraq's political progress.

GRADUAL WITHDRAWAL

Bitter sectarian conflict has killed tens of thousands of Iraqis since the U.S.-led invasion to topple Saddam in 2003 and threatened to tip Iraq into all-out civil war.

Rice briefed Maliki on U.S. President George W. Bush's Middle East tour and told him that a secure Iraq was vital for the stability of the region.

Iraqi government spokesman Ali al-Dabbagh said Rice had told Maliki that Bush wants to go ahead with a gradual troop withdrawal of 20,000-30,000 soldiers by the middle of this year.

He said Iraqi forces would be ready to take over security responsibility for all 18 provinces by the end of 2008. The U.S. military has so far handed back seven provinces to Iraq control.

"There will not be any imbalance because Iraqi forces are now capable of filling any vacancy made by withdrawals," Dabbagh said. "Iraqi forces will be responsible for the security file by the end of this year."

Rice had been with Bush before it was decided she should break away for a visit to Iraq while Bush went to Saudi Arabia.

"I decided I was in the neighbourhood and perhaps I should stop by," Rice said.

Maliki's government fractured last year with the withdrawal of the main Sunni Arab bloc as well as ministers loyal to anti-American Shi'ite cleric Moqtada al-Sadr.

The stalled political progress came at a time when significant security improvements were being made after the U.S. military poured the extra 30,000 U.S. troops into Iraq. Levels of violence are now down by about 60 percent since June.

Bush, who was briefed in Kuwait by U.S. commander in Iraq General David Petraeus and ambassador Ryan Crocker, said on Saturday the new strategy had reversed a descent into mayhem.