U.S. troops killed 12 militants during an "uptick" in fighting Sunday, the military said, as fierce clashes broke out in Baghdad's Sadr City district after radical cleric Muqtada al-Sadr warned he will declare war if a crackdown against his followers persists.

Secretary of State Condoleezza Rice, meanwhile, arrived in Baghdad on Sunday for a trip she said was intended to promote fresh political gains she sees to be flowing from the government-led assaults on radical militias.

Rice told reporters she sees signs that last month's assaults on militia forces in Basra have brought sectarian and ethnic groups together in an unprecedented way, and she said she wants to capitalize on that cohesion.

A loud explosion was heard in central Baghdad as a rocket or mortar shell was fired toward the U.S.-protected Green Zone as Rice was meeting with top Iraqi officials there. The area has faced regular shelling since the current tensions erupted last month.

The deadliest battle in Sadr City occurred just before 8 a.m. when gunmen attacked a U.S. checkpoint with machine guns, rocket-propelled grenades and mortar shells, a military spokesman said.

The Americans fought back, killing the seven militants, then shot to death two Iraqi snipers firing at them from a nearby rooftop as local nationals arrived to remove the bodies, according to the spokesman, Lt. Col. Steve Stover.

Three other militants were killed while trying to plant roadside bombs at about 6:43 a.m. elsewhere in Sadr City, Stover said.

He added that U.S. troops also clashed with militants elsewhere in Baghdad, but no deaths were reported in those incidents.

Sadr City, a sprawling district of some 2.5 million people in eastern Baghdad, has seen daily clashes between U.S.-backed Iraqi forces who have launched a crackdown against Shiite militias led by al-Sadr's Mahdi Army militia.

But Stover said the fighting on Sunday was among the fiercest.

"There was an uptick in violence in comparison with the past couple of weeks," Stover said, although he declined to link it to al-Sadr's warning, which was broadcast over mosque loudspeakers in the district late Saturday.

"We're not looking for a fight but what we are doing is protecting the Iraqi people," Stover said.

The deaths were in addition to seven armed "criminals" reported killed by the military on Saturday in Sadr City — two in gunbattles and five in two separate airstrikes.

Iraqi police and hospital officials also said six civilians — four men and two boys ages 8 and 10 — were killed in fighting in Sadr City after midnight.

The U.S. military insisted it does not engage if civilians are seen in the area and blamed the militants for putting innocent Iraqis at risk by mingling among them.

Internal Shiite rivalries have intensified since U.S.-backed Prime Minister Nouri al-Maliki launched a crackdown on March 25 against militias. The government also has demanded that al-Sadr disband his Mahdi Army militia or face political isolation, while insisting that military operations are only targeting criminal gangs.

Al-Sadr's followers believe the campaign is aimed at weakening their movement to prevent it from winning provincial council seats at the expense of Shiite parties that work with the United States in the national government.

Sadrist lawmakers, who hold 30 seats in the 275-strong parliament, demanded Sunday that the military operations stop in Sadr City and other Shiite areas and warned that they would continue to resist calls to disband the Mahdi Army.

"Random airstrikes, killings and bloodshed will not help but rather will increase hatred and enmity," Sadrist lawmaker Fawzi Akram said, reading a statement issued by the bloc.

Clashes also spread to the southeastern Shiite district of New Baghdad in the hours after al-Sadr's statement, wounding three people, police said.

A roadside bomb targeting a U.S. military convoy in the eastern Baladiyat area killed a child, Stover said.

Iraqi security forces also stormed into the local Sadrist office Sunday morning in Aziziyah, 35 miles southeast of Baghdad, detaining four people and confiscating computer disk drives and documents, police said.

A curfew was lifted farther south in the Shiite city of Nasiriyah as police raised the death toll from clashes there to 32 — 25 militia fighters and seven policemen — and said 40 suspects had been detained.

In the warning posted Saturday on his Web site, al-Sadr said he had tried to defuse tensions by declaring a unilateral truce last August, only to see the government respond by closing his offices and "resorting to assassinations."

He accused the government of selling out to the Americans and branding his followers as criminals.

"So I am giving my final warning ... to the Iraqi government ... to take the path of peace and abandon violence against its people," al-Sadr said. "If the government does not refrain ... we will declare an open war until liberation."

A full-blown uprising by al-Sadr, who led two rebellions against U.S.-led forces in 2004, could lead to a dramatic increase in violence in Iraq at a time when the Sunni extremist group al-Qaida in Iraq appears poised for new attacks after suffering severe blows last year.

The terror network on Saturday also announced a one-month offensive against U.S. troops and Sunnis who have joined forces with the Americans in a new Internet audiotape by the purported leader of al-Qaida in Iraq, Abu Ayyub al-Masri.

Underscoring concerns that Sunni insurgents are regrouping in the north, gunmen on Sunday ambushed three minibuses carrying university students near Baqouba, 35 miles northeast of Baghdad, and kidnapped their drivers although the students were released, police said.