U.S. tanks were seen heading to the area followed by sounds of explosions in fighting a day after Shiite cleric Muqtada al-Sadr, who has led an uprising against the U.S.-led occupation, warned that he would fight "until the last drop of my blood has been spilled."
On Tuesday, U.S. forces urged Najaf's residents to cooperate.
"We ask residents to cooperate with the Iraqi army and police," said a voice in Arabic through a loudspeaker Tuesday in Najaf. "There will be no truce or negotiations with terrorists."
In other recent developments:
Meanwhile, a militant group threatened to launch a campaign of attacks against Iraqi government offices and warned public employees not to go into work. The group, calling itself the Divine Wrath Brigades, said its "military rebellion and the shelling" would start Tuesday against state buildings.
"We warn all civilian government employees and others ... against going to the offices and institutions where they work because they could be subjected to shelling," the group said in a statement released Monday.
In its statement, the Divine Wrath Brigades claimed responsibility for a number of recent attacks on government ministries, U.S. military bases, hotels housing foreign journalists and contractors and the Green Zone — home to the U.S. and British embassies as well as Iraqi government offices.
The statement was read out by a masked gunman shown among a number of militants in another videotape obtained by APTN.
The group's claim could not be independently verified.
The uprising by al-Sadr's Mahdi Army began to affect Iraq's crucial oil industry, as pumping to the southern port of Basra — the country's main export outlet — was halted Monday because of militant threats to infrastructure, an official with the South Oil Company said.
About 1.8 million barrels per day, or 90 percent of Iraq's exports, move through Basra, and any shutdown in the flow of Iraq's main money earner would badly hamper reconstruction efforts. Iraq's other export line — from the north to Turkey — is already out of operation.
In southern Iraq, clashes intensified around Basra, where a British soldier was killed and several others wounded in fighting with militia near the cleric's office Monday, the British Ministry of Defense said. Three militants were killed and more than 10 others wounded, a senior Iraqi police official said.
In the holy city of Najaf, the main scene of fighting, U.S. forces tried once more to drive militiamen out of a sprawling cemetery, and an American tank rattled up to within 400 yards of the Imam Ali Shrine, Najaf's holiest site, which fighters have reportedly been using as a base.
Al-Sadr's vow to keep fighting was a defiant challenge to Allawi, who visited Najaf on Sunday and called on the Shiite militants to stop fighting.
"I will continue fighting," the young, firebrand cleric told reporters in Najaf. "I will remain in Najaf city until the last drop of my blood has been spilled."
President Bush said Monday that coalition forces were "making pretty good progress about stabilizing Najaf."
U.S. military officials estimated that 360 insurgents were killed from Thursday, when fighting began, and Sunday night, a figure the militants dispute. Five U.S. troops have been killed in the fighting. About 20 police also have been killed, Najaf police chief Brig. Ghalib al-Jazaari said.