US military reports that 25 soldiers died in a series of clashes on Saturday.
Hakim Al-Zameli, the deputy health minister, said that 156 people were wounded in the Baghdad attacks.
A few hours later at least 12 people were killed and more than 40 were wounded when a bomb exploded in a market in the predominantly Shia village of Khalis, near Baquba.
A mortar shell hit the market minutes later.
Hoda Abdel-Hamid, Al Jazeera’s correspondent in Baghdad, said: “Double attacks are now very common. A secondary bomb usually targets those running to help the victims of the first one.
“People here were fearing a wave of revenge attacks in the wake of Saddam Hussein’s execution. It now seems it is well under way. Car bombs are usually attributed to Sunni armed groups and Saddam loyalists.”
Iraqi police have reported that the mayor of Baquba has been kidnapped by Sunni fighters.
The city, 100km northeast of Baghdad, has been the scene of heavy fighting between its Sunni and Shia inhabitants.
Police said Khalid al-Sanjari was abducted from his office at about 1pm local time.
The US military in Baghdad said they were checking the reports.
In other news, a US soldier was killed by a roadside bomb in northern Iraq on Monday, bringing to 28 the number of US troops killed in the past three days.
The same day CNN television reported that military sources have said that a US helicopter which killed 12 soldiers when it crashed on Saturday may have been brought down by an “insurgent-fired” missile.
An al-Qaeda-linked coalition of Iraqi fighters claimed on Monday that its fighters shot the helicopter down.
In Washington, a senior US military official said investigators had found debris near the crash scene that could belong to a shoulder-fired weapon which may have been used to shoot down the helicopter.
Early on Monday, Iraqi forces backed by US troops sealed off Adhimiya, a predominantly Sunni neighbourhood of Baghdad, but the defence ministry said this was not the start of a promised new offensive.
Residents of the area in northern Baghdad said Iraqi soldiers had set up checkpoints on roads leading into the area and were preventing motorists from passing through.
They said the operation followed several nights of shooting.
US troops in armoured Stryker vehicles were also seen, other witnesses said.
They reported seeing residents walking out of the district on foot towards a nearby highway to catch lifts from passing cars.
Source: Al Jazeera, News Agencies