Twenty-five Iraqi soldiers have died in clashes with Shia militiamen in southern Iraq, hospital sources say.
The fighting broke out on Sunday night after troops conducted raids against a splinter group of Moqtada Sadr's Mehdi Army in the city of Diwaniya.
In the capital Baghdad, at least 14 people were killed in a suicide car bombing by Iraq's interior ministry.
The violence comes a day after at least 47 people were killed in a series of insurgency attacks across Iraq.
A spokesman for the Diwaniya general hospital said 34 bodies had been brought in - 25 Iraqi soldiers, seven civilians and two militiamen. He said at least 70 people were injured.
Local leaders are quoted as saying the gunmen in Diwaniya have split from the from the Mehdi Army after rejecting a call from their radical leader to take part in Iraq's political peace process.
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.
'Improved security'
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.
"Each time I come, I see more progress"
"The violence is on the decrease, and our security ability is increasing," Mr Maliki told CNN.
The bomber struck as UK Defence Minister Des Browne was in Baghdad 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.
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