Amid the tension, two ministers in the US-backed interim government escaped bombings in the capital, one of which was claimed by the group linked to Iraq's alleged Al-Qaeda chief, Abu Mussab al-Zarqawi.
Hundreds of heavily-armed Iraqi national guardsmen and US marines were seen fanning out across the Old City around the shrine well before nightfall.
At around 7:30 pm (1530 GMT), two US Apache helicopters fired missiles near the city's vast Valley of Peace cemetery, before tanks began pounding positions in the Old City around 10:50 pm, an AFP correspondent witnessed.
Artillery fire could also be heard coming from the direction of Najaf's twin city of Kufa, 10 kilometres (six miles) away.
Less than a week before Monday's anniversary of the birth of Ali, Shiite Islam's first and most revered imam, an assault to rid his mausoleum of militiamen looked imminent.
"This is the first day they are here and they will be staying here," said Lieutenant Haider Hassan Wahid, estimating that some 100 Iraqi troops, pulled together from an amalgam of security forces, were deployed in the Old City.
In the morning, Iraqi national guardsmen and US troops came under a hail of gunfire from the Mehdi Army as they marched down Medina Street which runs parallel to the mausoleum, one of the holiest Shiite shrines in the world.
"If Moqtada Sadr surrenders, he will be safe and sound. If he resists, the only thing for him is death or prison," Defence Minister Hazem al-Shaalan told the television cameras at a US military base outside the ravaged city.
"A large Iraqi force will near the mausoleum, waiting for the signal for the assault, unless they surrender. There are only a few hours left," said Shaalan.
With the combined US-Iraqi force within 350 metres (yards) of the Imam Ali, aides of the militia leader said he was ready to re-negotiate peace but would not accept humiliation after the 20-day conflict.
"We are ready now to negotiate again," Ali Smeisim told reporters.
"We will not accept any solution that is humilitating for us... these threats will lead to more destruction and chaos," said Sheikh Ahmed al-Shaibani, reiterating a readiness to deliver the shrine to the Shiite religious leadership.
Despite announcing four days ago they would hand over control of the shrine to representatives of the most revered Shiite cleric, Grand Ayatollah Ali al-Sistani, the agreement has since stalled.
Najaf governor Adnan al-Zorfi, who has championed the use of US troops in an effort to flush the Mehdi Army out of what was once a glorious pilgrimage city, said Iraq's national guard were ready to evict militiamen from the shrine.
"We are going to cleanse the city and the shrine of militiamen if they do not leave soon of their own accord," he told AFP.
Serious damage to the mausoleum could inflame the already tense standoff. A hole one metre (more than three feet) across was already punched into the outer wall of the shrine compound late Sunday night.
Further south, in the city of Amara, 12 Iraqis were killed, including three children, and 54 people wounded during afternoon clashes between the Mehdi Army and British troops, hospital sources said.
Back in Baghdad, four bodyguards were killed when a suicide bomber blew up a car near Environment Minister Mishkat al-Moumin, in an attack attributed to Zarqawi loyalists on an Islamist website.
Three passers-by and another guard were wounded when the bomber was prevented by Moumin's security detachment from smashing into her vehicle as she left her highly fortified residential compound, bodyguard Shamil Kamel said.
Just 30 minutes later, a roadside bomb exploded in eastern Baghdad alongside the convoy of Education Minister Sami al-Mudhaffar, killing one guard and wounding two others, his office said.
Assassination attemps against Iraqi ministers are frequent, despite stringent security precautions taken by leading officials.
A US soldier was also killed in the capital Monday, bringing to at least 716 the number of US troops killed in action in Iraq since last year's invasion.
West of Baghdad, US planes flattened a suspected foreign fighters' hideout near the notorious Sunni insurgent bastion of Fallujah, with the approval of Prime Minister Iyad Allawi, the military said.
Meanwhile, the Italian government insisted it would maintain its 3,000 troops in Iraq despite an ultimatum from an Islamic group holding an Italian journalist demanding that Rome withdraw its forces within 48 hours.
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