(Adds defence spokesman)

BAGHDAD, July 2 (Reuters) - A roadside bomb exploded near an Iraqi army patrol in Baghdad on Thursday, police said, killing one soldier and wounding 10 people.

The bomb was the first in Baghdad since U.S. troops pulled out of city centres on Tuesday, police said.

That withdrawal was a milestone in a bilateral security agreement that calls for the U.S. forces which invaded Iraq in 2003 to topple Saddam Hussein to leave the country by the end of 2011. Around 130,000 troops still remain.

The blast took place in the riverside Abu Nawas area of central Baghdad during the morning rush hour. Two of the wounded were soldiers.

Police said there had been no bombings in the Iraqi capital on Wednesday, the first day that the city's security became entirely the responsibility of Iraqi police and troops.

Interior Ministry spokesman Abdul-Karim Khalif said no Iraqis had died in violence on Wednesday throughout the country.

It was not immediately possible to verify these claims, but no major incidents were reported in Baghdad on Wednesday.

"We congratulate ... the Iraqi people for turning the first page of the timetable for the withdrawal of U.S. forces from Iraq, which concluded peacefully and without obstacles," Defence Ministry spokesman Mohammed al-Askari said.

He said the next step was to cut the size of U.S. forces. President Barack Obama has pledged to pull all combat troops out of Iraq by September 2010, leaving only advisers and trainers.

Police said some checkpoints had been lifted on Thursday and some blocked roads opened up.

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 to try to exploit the U.S. pullback to test Iraqi defence forces, whose progress has been fitful since they were disbanded in 2003 and rebuilt from scratch.

Maliki's government insists they are now ready for the challenge.

"We have full confidence that security will improve in Iraq," Askari said. "We will not give a chance for the terrorists to pause for breath. Iraq will witness a big improvement in the security situation in the coming days."

The leader of the Islamic Army in Iraq, thought to be the military wing of Saddam's outlawed Baath party, said 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 and Tim Cocks; editing by Robert Woodward)

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