One of the blasts in Ur district went off near a market, police said. The attacks took place at sunset on Monday shortly before Iftar, when Muslims break their fast during the holy month of Ramadan.
The brother of Munqith al-Faroon, the chief prosecutor in the genocide trial of deposed Iraqi leader Saddam Hussein, was also murdered on Monday in west Baghdad, a government official said.
Emad al-Faroon was returning to his home in the west Baghdad neighbourhood of Jamaa with his wife when he was surprised by gunmen and shot dead, said Ali al-Lami, the head of the de-Baathification committee and a close friend of al-Faroon.
The fresh violence came as George Bush, the US president, assured Nuri al-Maliki, the Iraqi prime minister, that Washington had not set any deadline for the Iraqi government to get control of sectarian violence threatening to plunge Iraq into civil war.
US and Iraqi forces have launched a security crackdown in Baghdad in a bid to ease sectarian violence gripping the capital, but bloodshed has continued unchecked.
Saddam meanwhile has urged Iraqi fighters to be merciful to their US and Iraqi enemies, telling them in an open letter that they are close to driving foreign forces out of Iraq.
"The hour of liberation is at hand, God willing, but remember that your near-term goal is confined to freeing your country from the forces of occupation and their followers and not to be preoccupied in settling scores"
deposed Iraqi leader
In a three-page letter obtained on Monday, Saddam urged Iraq's majority Shia population and its Sunni minority to set aside their differences and focus instead on driving the US forces out of Iraq.
"The hour of liberation is at hand, God willing, but remember that your near-term goal is confined to freeing your country from the forces of occupation and their followers and not to be preoccupied in settling scores," Saddam wrote in the Arabic-language letter, which he dictated to his lawyers at the weekend and signed as the "President and commander in chief of the holy warrior armed forces".
In other incidents of violence, four civilians were killed and another seven injured in a random shooting near a bus terminal in the rural town of Khalis, 25km north of the provincial capital Baquba.
The shooting followed an overnight blast outside a Shia mosque in Khalis, that wounded seven people.
Just outside Khalis, shots were fired at a policeman, killing him and a nearby civilian.
Whilst northeast of Baquba, in the town of Muqdadiya, gunmen killed two civilians.
Police also reported finding the bound corpses of three policemen who had been kidnapped on their way back from a training course in Jordan.
Another three bodies turned up in Baquba itself, which was also the scene of the shooting death of another civilian.
The US military headquarters on Monday announced that seven more of its troops have been killed in action in Iraq, bringing the number of American troops to have died this month to 57.
A statement from the US-led coalition in Iraq said that two marines from Regimental Combat Team 5, which is based in Falluja in western Iraq, died on Sunday following unspecified "enemy action".
Another statement said that an army soldier "was killed at approximately 10.45 pm [1945 GMT] on Sunday when the vehicle he was riding in was struck by an improvised explosive device north of Baghdad".
And two more soldiers were killed and two others wounded on Sunday "as a result of enemy action while conducting operations in Kirkuk province", it said.
Another two soldiers from the the same Task Force Lightning died in the central Salaheddin province of wounds sustained in fighting.
The deaths bring the number of US military personnel to have died in the Iraq campaign since the March 2003 invasion to 2,766, according to an AFP count based on Pentagon figures.