Iraq's interim prime minister has ordered militants in the holy city of Najaf to lay down their arms as he made a brief, unannounced visit.
Allawi stepped into the heart of the recent bitter clashes
Gunfire and explosions were heard during Iyad Allawi's trip as US forces and militants clashed for a fourth day.
The government has offered low-level criminals an amnesty in an effort to quell the 16-month-old insurgency.
But it has brought back the death penalty for crimes including murder, kidnapping and drug dealing.
The Iranian government has confirmed that one of its diplomats has gone missing in Iraq and is feared kidnapped.
A group calling itself the Islamic Army in Iraq released a video showing Fereidoun Jahani's passport and said he had been trying to incite sectarian strife.
Speaking to reporters in Najaf, 160km (100 miles) south of Baghdad, a heavily-guarded Mr Allawi said there would be no negotiations with "any militia that bears arms against Iraq and the Iraqi people".
"The outlaws have to lay down their weapons and leave the city's holy sites including the Imam Ali shrine."
During his visit, fighters were still on the streets and US helicopter gunships circled overhead.
Correspondents say Mr Allawi also tried to strike a conciliatory note, saying he did not believe those people "committing the crimes" in Najaf were under the control of rebel Shia cleric Moqtada Sadr, but were common criminals.
A spokesman for Mr Sadr has insisted the uprising in Najaf is legitimate.
Both sides blame each other for the reigniting of hostilities in Najaf
The fighting in Najaf is the worst since a ceasefire between US forces and Shia militants was agreed in June. Scores of people have been reported killed since Thursday.
Hours after Mr Allawi's visit, mortar bombs and rockets struck a residential area of Baghdad. Reports say a 10-year-old boy was killed and a number of people wounded.
Correspondents say the amnesty offer and the reinstatement of the death penalty make up a carrot-and-stick approach to insurgents.
Capital punishment was suspended in Iraq after the toppling of Saddam Hussein.
The amnesty law, signed on Saturday, applies to those who possess small arms or explosives, or have sheltered wanted militants.
The BBC's Alastair Leithead says it does not apply to most of those involved in the fighting.
Mr Sadr led a two-month rebellion across several Iraqi cities beginning in April that was brought to a close with a series of truces after hundreds had died.
Both sides blame each other for reigniting hostilities.
The number of those who have died is unclear, with the US military claiming to have killed hundreds of militants and Mr Sadr's aides insisting that only some 37 men have died.
Fifty people have been killed and 300 wounded in bloodshed throughout Iraq over the past day, the health ministry said on Sunday.
As one of the holiest Muslim cities in the world, Najaf had reopened to pilgrims, and our correspondent says the dead are sure to include civilians.
The rebellious slum district of Sadr City in Baghdad is among other flashpoints in Iraq.
On Saturday, a spokesman for Kofi Annan said the United Nations secretary general was "extremely concerned" about the fighting in Najaf and was appealing for a new ceasefire.
His plea was echoed by Shia leaders, who threatened to boycott an upcoming political conference if the violence did not end.