The seven Multinational Division - Baghdad soldiers were killed and 11 others wounded in a western section of the capital, the military said in a statement. Two prisoners detained previously and being transported were killed in the accident, and a third was injured, the military said.
The military said it did not immediately have further details.
Another soldier was killed and two more were injured east of Baghdad in a non-combat incident when their vehicle overturned and caught fire, according to a separate statement.
The cause of both accidents are under investigation, the military said.
A Task Force Lightning soldier also died from injuries sustained during an attack Sunday in northern Iraq, the U.S. command said. The soldier's patrol came under rocket fire in the Kirkuk area.
Meanwhile, Prime Minister Nouri al-Maliki told lawmakers Monday that Iraqi forces were not ready to take over security from the U.S. military across the country.
"There have been tangible improvements in security in the recent period in Baghdad and the provinces but it is not enough," he told parliament. "Despite the security improvement, we still need more efforts and time in order for our armed forces to be able to take over security in all Iraqi provinces from the multinational forces that helped us in a great way in fighting terrorism and outlaws."
Al-Maliki made the comment hours before the U.S. ambassador to Iraq, Ryan Crocker, and top U.S. commander Gen. David Petraeus were to appear in the U.S. Congress to deliver reports on Iraq's progress amid a debate over calls to start bringing American troops home.
The two Americans were widely expected to maintain that this year's troop buildup has reduced violent attacks in Baghdad and argue for more time to restore security.
Al-Maliki said that violence had dropped 75 percent in the Baghdad area since the U.S. began pouring in additional troops at the start of the year. He gave no figures.
"The key to reconstruction, economic development and improving peoples' standard of living is security," he said.
Still, attacks in the capital have picked up in recent days in the run-up to the report and as the Muslim holy month of Ramadan nears, a time when violence usually spikes higher.
CBS News chief foreign correspondent Lara Logan reports that most Iraqi citizens seem to disagree with the positive assessments of the troop surge.
"You only have to look at the number of Iraqis trying to flee the country every day to know they don't feel safer," Logan said on CBS' Early Show. "They don't believe any gains being made in security are enduring."
Evidence of Iraqi citizens' lack of confidence in improvements heralded by the U.S. military was also reported Monday by the British Broadcasting Corporation.
A poll of about 2,000 ordinary Iraqis by the BBC, in conjunction with ABC News and Japan's NHK, found that 70 percent believe security in the area covered by the troop surge has deteriorated in the last six months.
Sixty-percent of those polled also said attacks on U.S. troops in Iraq were justified.
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