Rebels loyal to Moqtada Sadr in Najaf say they are holding fresh talks with Iraqi religious leaders about the control of the Imam Ali shrine.
Tanks reportedly advanced after a night of heavy bombardment
But Mr Sadr, whose fighters are holed up at the shrine, is vowing to continue fighting US-led forces, an aide said.
Iraqi Prime Minister Iyad Allawi told the BBC troops would not attack the mosque to flush out Mr Sadr's fighters.
US tanks have reportedly encircled the shrine after an intense bombardment of rebel positions overnight.
In other developments in Iraq:
- Two US marines die in separate incidents in the restive Anbar province, west of Baghdad, the US military says
- US warplanes twice strike targets in Falluja, west of Baghdad, killing at least two people, according to hospital sources
- Suspected Sadr militants set fire to the headquarters of Iraq's South Oil Company in Basra
- The US embassy in Iraq is hit by mortar fire, slightly injuring two employees
- A new US army report on the Abu Ghraib prisoner abuse scandal will implicate at least two dozen more personnel, say US defence officials, and a report by a US academic says some medics collaborated with abusive guards.
The BBC's Alastair Leithead in Najaf said, apart from occasional mortar fire, the old city had fallen quiet on Friday after a night of fierce fighting.
US warplanes dropped bombs and tanks shelled rebel positions for five hours in the heaviest assault since fighting began two weeks ago.
The Iraqi health ministry said 77 people have been killed and 70 others wounded in fighting in Najaf since Thursday.
In a seemingly positive move, a spokesman for Mr Sadr, Sheikh Ali Shaibani, said a delegation was ready to hand over the keys to the Imam Ali mosque to aides of Iraq's most influential Shia leader, Grand Ayatollah Ali Sistani.
But Mr Shaibani said Mr Sadr would not comply with the government's demand to disband his Mehdi army and vowed to fight on.
"We will defend not only the Ali shrine, but also the holy city of Najaf, which is as sacred as Mecca," he told AFP news agency.
Our correspondent says the talk of deals, agreements and negotiations continues, but word from the mosque is that the fighting would go on.
Behind the increasing violence there is a war of words that still seems to be going nowhere, he adds.
Despite renewed fighting, Prime Minister Allawi said the "olive branch is still extended" to Mr Sadr.
Speaking to the BBC a day after issuing a "final call" for Mr Sadr's Mehdi Army to leave the shrine and disband, Mr Allawi said US-led forces would not launch an assault on the mosque.
"We are not imposing a military solution... We definitely are not going to attack the shrines," he said.
"We have extended and still extend an open hand to Moqtada Sadr.
"He can join the political process and he is welcome to."
Mr Allawi said fighters sheltering in the shrine included "ex-criminals [who] have wired up the holy shrine to blow it up".
Al-Qaeda fighters were also inside, he said.