The Iraqi health ministry said on Sunday 22 people died in clashes in Baghdad's suburb, Sadr City, and other parts of the capital from 9am (0500 GMT) on Saturday to 9am on Sunday.
At least 21 people were killed in similar clashes in Najaf during the same period.
"The figures from Najaf are initial because there are still bodies that could not be collected due to the ongoing fighting," an official said.
Iraqi Shia leader Muqtada al-Sadr's Mahdi Army militia has been battling US occupation forces since Thursday. Residents said the flashpoints in Baghdad and Najaf were relatively calm on Sunday morning.
Flashpoints in Baghdad and
Najaf were calm on Sunday
A security source said one Iraqi national guardsman was killed and another wounded on Sunday when a roadside bomb hit their patrol north of Baghdad.
Several loud explosions rocked the capital on Sunday morning, but their cause was not immediately clear, said the occupation force.
At least 20 mortar bombs fell in the centre of the capital without causing injuries or damage throughout Saturday night.
In another incident, a US military helicopter made an emergency landing on Sunday northwest of Baghdad near Sadr City, the US military said.
"The figures from Najaf are initial because there are still bodies that could not be collected due to the ongoing fighting"
Health ministry official, Iraq
"An OH-58 Delta had a precautionary landing northwest of Sadr City; both pilots are safe," Major-General Peter Chiarelli said, adding the helicopter was not attacked and it was a maintenance issue.
In the northern city of Kirkuk, a seven-year-old Iraqi child was killed and three others injured when they were caught by a roadside bomb on Sunday.
The children, aged five to 10, were on their way to a playground next to their home in the centre of Kirkuk when they accidentally stepped on the bomb, said Iraqi police Colonel Sirhat Qadir.
Meanwhile, the body of a prominent Kurdish businessman in Kirkuk was found stabbed to death in the predominantly Arab town of al-Riad, west of the city, according to Lieutenant-Colonel Imad al-Ubaidi.
In Baquba, an Iraqi national guardsman died and another was injured late on Saturday as security forces were attempting to defuse a bomb on the road to the village of Kanaan, southeast of the city.
Attacks on Iraqi police and national guardsmen are frequent in Baquba, 60km southeast of Baghdad. A car bomb attack on a police station in Baquba's centre at the end of June killed 70 people, mostly police recruits.