BAGHDAD, July 2 (Reuters) - A roadside bomb blew up as an Iraqi army patrol passed by in Baghdad on Thursday, killing one soldier and wounding 10 two days after U.S. troops pulled out of cities and handed security to their local counterparts, police said.

The bomb was the first in Baghdad, police said, since Tuesday's partial U.S. withdrawal, a day labelled "National Sovereignty Day" by Iraqi authorities elated at what they see as a major step to shaking off a foreign occupation.

The pullback from urban centres is a major milestone in a bilateral security agreement that calls for the last of the U.S. soldiers who invaded Iraq in 2003 to topple Saddam Hussein to leave the country by the end of 2011.

The blast on Thursday took place in the Abu Nawas area of central Baghdad during the morning rush hour.

Police said there had not been a single bombing in the Iraqi capital on Wednesday, the first day the security of the inner city became entirely the responsibility of Iraqi police and troops. They said some checkpoints had been lifted on Thursday and some blocked roads opened up.

It was not immediately possible to verify the claim that the bomb was the first but no major incidents were reported in Baghdad on Wednesday.

Violence across Iraq has fallen sharply since the peak of sectarian bloodshed in 2006-07, but insurgents such as al Qaeda continue to stage devastating attacks.

The number of civilians who died violent deaths jumped in June to 373, up from a low of 134 in May, after a spate of major bombings in Baghdad and the northern city of Kirkuk -- including two of the deadliest bomb attacks in more than a year.

U.S. and Iraqi officials say they expect insurgents and militants to try to take advantage of the U.S. pullback to launch more attacks and to test the Iraqi defence forces.

The leader of the Islamic Army in Iraq, thought to be the military wing of Saddam's outlawed Baath party, claimed the U.S. withdrawal was a victory not for the Iraqi government but for insurgents, according to the SITE Intelligence Group.

"If anyone has a right to celebrate victory, it should be the resistance and its men and those who rallied around it and supported it among the children of our people and our Ummah (nation)," the "emir" of the group said in an online message monitored by SITE.

"They are the ones who brought the occupation to a despicable defeat and made their remaining forces in Iraq demanding and very costly." (Reporting by Aseel Kami; Writing by Michael Christie; Editing by Charles Dick)

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