The raids took place in and around Yussifiyah, a town about 20km south of Baghdad, where an American helicopter apparently was shot down by insurgents nearly a month ago, killing two soldiers on board, the US army said on Sunday.
The army did not say whether any of the 20 it killed had been involved in the April 1 crash.
The toll includes 12 insurgents, at least five of them foreign, who were killed in Yussifiyah on Tuesday when US troops backed by a helicopter and jets struck a suspected safehouse there, the military said.
It also said it had captured seven militants and detained more than 50 suspects on Saturday.
It said insurgents have been using Yussifiyah, the scene of numerous ambushes against US and Iraqi troops, foreigners and Shia civilians, as a staging area to conduct suicide attacks in Baghdad.
Also on Sunday, insurgents killed three Iraqis, and the bullet-ridden bodies of seven Iraqi men were found in the capital.
A roadside bomb hit a US military convoy in central Tikrit, near the hometown of Saddam Hussein, a police official said.
He said the blast set a Humvee on fire, causing US casualties, but the US command could not immediately confirm the report.
In Ramadi, 115km west of Baghdad, gunmen attacked three police officers travelling in a car carrying the salaries of police in Fallujah, killing one, wounding another, and kidnapping the third with the bag of money, police said.
The US command updated the American death toll for April to at least 70 people killed – the highest monthly figure since November, when 84 Americans died.
In Baghdad, Nuri al-Maliki,the prime minister-designate, met politicians to choose his cabinet for a national unity government.
The US and its Iraqi allies hope that the future government will bring back stability to the war-ravaged country by calming sectarian tensions and luring disaffected Sunni Arabs away from the insurgency.
Al-Maliki has promised to finish the job in a fortnight, but it could be difficult to find politicians who have enough power and aren't linked to militias that are blamed for sectarian violence.
In an interview on Saturday with America's National Public Radio, Zalmay Khalilzad, the US ambassador, said of al-Maliki: "It's good to have a deadline, but I think perhaps he's being optimistic. It will be tough for him."