Iraqi troops have fought battles with Shia militiamen in the southern town of Diwaniya, amid an upsurge in violence in which dozens of people have died.
The fighting prompted some local people to flee Diwaniya
At least 19 soldiers were killed and more than 40 people were wounded in Diwaniya. Officials said some 40 gunmen from the Mehdi Army had also died.
Government forces had lost control of parts of the city, officials said.
In Baghdad, 11 people died when a suicide car bomber attacked a compound of the Iraqi interior ministry.
A spokesman for the Diwaniya general hospital said 34 bodies had been brought in, including soldiers and seven civilians and two militiamen.
Local leaders are quoted as saying the gunmen in Diwaniya have split from the Mehdi Army after rejecting a call from their radical leader to take part in Iraq's political peace process.
Members of the militia have set up their own checkpoints in the town, eyewitnesses said, and the government has sent large numbers of reinforcements.
In Baghdad, dozens of people were injured in the mid-morning blast outside the interior ministry.
The ministry complex has been frequently targeted in the past and is heavily guarded. At least eight policemen are reported to be among the fatalities.
Insurgents have carried out almost daily attacks against Iraqi and coalition targets since the US-led invasion of Iraq in March 2003.
Thousands of Iraqis have died in apparently sectarian attacks in the past four months alone.
However, a US general says violence has fallen in Baghdad by nearly a half since July, although he acknowledged a spike in bombings in the past 48 hours.
"Insurgents and terrorists are hitting back in an attempt to offset the success of the Iraqi government and its security forces," Maj Gen William Caldwell told reporters.
The Baghdad bomber struck as UK Defence Minister Des Browne was in the capital for talks with Iraqi officials.
After meeting Iraqi Defence Minister Abdul-Qader Mohammed Jassim al-Mifarji, Mr Browne said Iraq was moving forward.
"Each time I come, I see more progress," he said.
Meanwhile, five US soldiers were killed in two separate bomb attacks in Iraq on Sunday afternoon, the US military said.
Four soldiers died when a roadside bomb hit their vehicle north of Baghdad, a military statement said.
A fifth soldier was killed when a roadside bomb struck his vehicle in the west of the capital.