Attackers in a car opened fire on Monday on a police patrol in the eastern New Baghdad neighbourhood of the capital, killing two policemen, police 1st Lieutenant Ali Abaas said.
In a separate attack in the same neighbourhood, police Colonel Alaa Hussain was killed near his home late on Sunday, Abbas said.
Elsewhere on Monday, armed fighters gunned downed Maissa Jassim, a worker for the Iraqi Trade Minister, in the southern neighbourhood of Dora, Dr Muhanad Jawad of the Yarmuk hospital said.
Al-Qaida in Iraq said one of its "field commanders" had been killed by forces in western Iraq, the group purportedly said in a statement posted on a website used by militants. The statement did not say when the man, Abi Salih al-Ansar, was killed.
On Sunday, four car bombs killed 22 people, including five election employees and one policeman in an attack on the offices of Iraq's electoral commission.
Ayat Allah Sistani is said to be
upset by the upsurge in attacks
The commission said in a statement that it "affirms its determination to continue the electoral process", including plans for a national referendum on a new constitution and balloting for a new government later this year.
The government also said on Sunday that more than 90 people had been killed in a bombing attack the night before near a Shia mosque in al-Musayyib, 65km south of Baghdad. Hospital officials said more than 150 were injured in the blast.
Iraq's top Shia cleric, Grand Ayat Allah Ali al-Sistani, was deeply upset by the upsurge in attacks, said Vice-President Adel Abd al-Mahdi, a top Shia politician, after meeting him on Sunday.
The cleric urged the government to protect the people in "this genocidal war", Abd al-Mahdi said.
At least 170 people have been killed in bombings throughout Iraq in the past week.
The US military also reported on Sunday that three of its soldiers had died in separate bombings over the weekend.
On Monday, a university professor was buried in the southern Iraqi city of Basra, a day after being killed by unknown attackers.
Alaa Daud Salman, history professor at Basra University, was shot dead late on Sunday in the central neighbourhood of Ashar, said his relatives and colleagues who attended the funeral.
Salman was a Sunni Muslim and a former member of Saddam Hussein's Baath Party. During Saddam's rule, he was the head of the history department at the university but lost that post after the fall of the Baath regime in April 2003.
Attacks against university professors were common after Saddam's overthrow because many of them had close ties to his regime.
But it was not clear if Salman's killing was linked to tensions between Iraq's Shia and Sunni communities. Basra is mostly Shia.