BAGHDAD, Iraq (CNN) -- Three U.S. soldiers were killed and 31 others wounded in two rocket attacks Sunday afternoon in Baghdad, the U.S. military said.

Mehdi Army militiamen celebrate after attacking an Iraqi Army vehicle in Baghdad's Sadr City on Sunday.

Earlier Sunday, fighting between U.S. troops and the Mehdi Army militia loyal to Shiite cleric Muqtada al-Sadr left at least 20 dead and 52 wounded in Baghdad's Sadr City, according to an Iraqi Interior Ministry official.

The U.S. military said it had no information about the Sadr City fighting.

Sunday's violence came as Iraqi Prime Minister Nuri al-Maliki demanded al-Sadr disband his Mehdi Army and threatened to bar al-Sadr's followers from the political process if the cleric refused. Watch a report from the front line in Sadr City »

"A decision was taken yesterday that they no longer have a right to participate in the political process or take part in the upcoming elections unless they end the Mehdi Army," al-Maliki said.

Sunday's American fatalities bring the death toll of U.S. troops in the Iraq war to 4,022; that toll includes eight civilian contractors working for the Pentagon. Nearly 30,000 others have been wounded in action.

An attack involving a "couple of rounds" of fire on the International Zone, also known as the Green Zone, killed two soldiers and wounded 17 others about 3:30 p.m., a military official said, declining to give the specific location of the attack for security reasons.

A separate attack about 30 minutes earlier killed one soldier and wounded 14 at a U.S. military outpost in Rustamiya in southeastern Baghdad, the military said.

Responding to al-Maliki's comments, a spokesman for al-Sadr, Sheikh Salah al-Obeidi, said that any effort to bar Sadrists from participation in politics would be unconstitutional -- and that any decision to disband the Mehdi Army is not the government's to make.

"It is up to the side that established it," he said.

Al-Maliki spoke in an exclusive interview with CNN after a weeklong military offensive against what Iraqi officials called gangs and militia members in the southern Iraqi city of Basra.

Hundreds were killed or wounded in the fighting across Iraq, which reportedly ended when Iranian and Iraqi Shiite officials held talks in Iran with al-Sadr.

Asked about Iran's role in ending the Basra conflict, al-Maliki attributed the cease-fire to the work of his security forces. Haidar al-Abadi, an Iraqi lawmaker who belongs to al-Maliki's Dawa Party, said last week that Iranian officials participated in the discussions, and another source close to the talks said the Iranians pressured al-Sadr to craft an agreement.

"I am not aware of such an attempt," al-Maliki said Sunday. "What happened on the ground and the breakdown in the structure of this militia is what made Muqtada al-Sadr issue his statement to withdraw his militants from the streets. What happened was something to save Muqtada, not to help us." Watch al-Maliki talk about issues that concern Iraq »

In northern Iraq, security forces detained a suspect Sunday and were searching for others in connection with the kidnapping of 42 college students, authorities said.

Gunmen seized the male students in northern Iraq before releasing them several hours later, according to a military spokesman and police in Nineveh province.

None was harmed, according to the U.S. military.

Gunmen stopped two buses loaded with students who were on their way to college, but one bus managed to escape, police said. Four students on the bus that escaped were wounded by gunfire, police said.

Students on the other bus were released Sunday afternoon after coalition military forces spotted the bus during an air patrol on the western outskirts of Mosul, according to a U.S. military news release.

The kidnappers fled the vehicle after it was stopped, according to a military press release.

Other developments

• A Christian priest was shot and killed in eastern Baghdad's Wihda neighborhood around noon Saturday, according to an Iraqi Interior Ministry official. The priest was identified as Father Yousif Adel. He belonged to St. Peter and Paul's Assyrian Orthodox Church.

• At least two people were killed Saturday and 16 others wounded when a bomb exploded in a minibus in eastern Baghdad's Beirut Square, the official said.

• President Bush is planning to address the nation Thursday morning about the Iraq war, sources said. Bush is expected to address the administration's decision to reduce combat tours of duty from 15 months to 12 months, Republican and Democratic sources said. E-mail to a friend

CNN's Nic Robertson, Jomana Karadsheh and Ingrid Formanek contributed to this report.

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