Radical Shia cleric Moqtada Sadr has offered to end an uprising in the Iraqi holy city of Najaf.
Fighters loyal to Moqtada Sadr remain defiant
However, Mr Sadr says there must be a truce before his Mehdi militia will leave the Imam Ali shrine and disarm.
Fighting is continuing in Najaf, where Mr Sadr's forces have battled US-led troops for nearly two weeks.
Meanwhile, US forces say they have made a big incursion into Sadr City, a predominantly Shia district of the capital, Baghdad.
A US tank was reportedly badly damaged during the assault on the suburb and one US soldier was wounded.
Iraqi militants who say they captured a US journalist last week are said to have threatened to kill him if US forces do not leave Najaf.
The first indications that Mr Sadr was offering to withdraw from the Imam Ali shrine came during a national conference in Baghdad to select an interim Iraqi council.
As delegates met for an unscheduled fourth day on Wednesday, one of the organisers of the meeting read out a letter which she said she had received from Mr Sadr, in which he accepted the national conference's terms.
These also included joining the political process in exchange for an amnesty, she said.
The previous day, Mr Sadr had refused to see a peace delegation sent by the conference, citing concerns over security and the status of the delegates.
One of Mr Sadr's spokesmen, Sheikh Hassan al-Zerkani, told the BBC that the cleric's offer was genuine, but guarantees needed to come from the occupiers, not the occupied.
He said signs were needed from the Americans that they would not go after the Mehdi Army.
The Iraqi defence ministry later said Mr Sadr and his followers would be granted amnesty only after they abandoned their uprising in Najaf and other cities.
The BBC's Kylie Morris in Najaf reported that there was no sign of a ceasefire.
She said gunfire could be seen lighting up the night sky and police had warned people to stay indoors because of the danger.
Our correspondent in Najaf says Mr Sadr has shown himself a master of brinkmanship and bluff in the past - and whether he is sincere in his offer will only be clear when peace returns to Najaf.
Al-Jazeera television has broadcast a videotape of an armed group threatening to kill US journalist Micah Garen unless US forces withdraw from Najaf.
The footage showed a man with a moustache kneeling in front of a group of five masked men holding rifles.
US-led troops have been fighting Sadr forces for nearly two weeks
The channel said the group called itself the Martyrs' Brigades.
Mr Garen, founder and head of Four Corners Media, is reported to have been kidnapped last Friday along with his Iraqi translator in the southern Iraqi city of Nasiriya.