(Adds mortar attack, paragraph 7)

By Paul Tait

BAGHDAD, Jan 15 (Reuters) - U.S. Secretary of State Condoleezza Rice praised Iraq on Tuesday for passing the first in a series of critical laws meant to reconcile warring Iraqis, saying progress was remarkable even though more was needed.

Rice, who has been travelling with President George W. Bush on his Middle East tour, gave one of the most upbeat assessments yet by a senior American official of political progress in Iraq during a surprise visit to Baghdad to meet Iraqi leaders.

Calling it a time of hope for Iraq, she said there seemed to be a "spirit of cooperation" between the leaders of the country's ethnic and religious groups, who have often frustrated Washington with their failure to agree on anything of substance.

Washington wants Prime Minister Nuri al-Maliki's Shi'ite-led government to match security gains with progress on political reconciliation between majority Shi'ite and Sunni Arab 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 batch 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 in Baghdad's heavily fortified Green Zone.

Five mortar bombs landed in the zone on Tuesday, police said, but there were no immediate reports of injuries. There had been a lull in such attacks in recent weeks.

The benchmark 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 little sign of progress on either bills.

"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

Foreign Minister Hoshiyar Zebari said Iraq must capitalise on political and security progress that had made its neighbours less fearful of instability spreading through the region.

"We believe that this year we will witness better support from Arab states by increasing their representatives and presence in Iraq," Zebari told the same news conference.

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.

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

Iraq would be ready to take on security responsibility for all 18 provinces by the end of 2008, Dabbagh added. Coalition forces have handed back nine provinces to Iraqi control.

Bush told reporters in Riyadh he would not travel to Iraq on this trip but joined Rice in praising Iraq's leaders.

"The leadership is more confident. The grassroots is more involved ... The government is beginning to respond," he said. (Additional reporting by Waleed Ibrahim, Wisam Mohammed and Ahmed Rasheed in Baghdad and Matt Spetalnick in Riyadh; Editing by Ibon Villelabeitia)

AlertNet news is provided by