Iraq's interim leader Iyad Allawi has threatened an assault on Falluja if residents do not turn in Jordanian militant Abu Musab al-Zarqawi.
The US and Iraqi governments are aiming to retake rebel areas
Zarqawi, Iraq's most wanted man, is thought to be based there. His group has captured and killed hostages.
Mr Allawi told parliament in Baghdad that an attack would start if Zarqawi and his group were not handed over.
His words are being seen as the clearest threat yet against insurgents holding Falluja.
Bombs and talks
Falluja, a predominantly Sunni Muslim city of 300,000, has become a focal point of resistance to the US-led occupation.
US forces have staged weeks of what they call "precision strikes" aimed at targeting Zarqawi's fighters and other militant groups in the town.
Negotiations between government and Falluja leaders to try to find a peaceful solution have also been continuing but so far remain deadlocked.
The US and the Iraqi interim government are trying to retake the rebel areas ahead of elections planned for January.
Fighting between militants and US troops near Falluja left five Iraqis dead on Wednesday. Hospital sources said they died in explosions on the eastern edge of the town.
The US military said the clashes began when insurgents opened fire on American troops, who called in air support.
In other violence:
- Renewed clashes between insurgents and US forces in Ramadi
have left six Iraqis dead and 33 injured, hospital sources say
- A police captain was killed in a drive-by shooting near Baquba
- Two US soldiers died in the northern city of Mosul when a suicide bomber ploughs into their convoy, the US military said
- Separate attacks hours apart late on Tuesday and into Wednesday in Baghdad killed four American soldiers
According to the Pentagon, 1,079 American soldiers have been killed in Iraq since the start of the US-led invasion of the country in March 2003.
The United States has offered a $25m reward for Zarqawi's capture.
"If Zarqawi and his group are not handed over to us, we are ready for major operations in Falluja," Mr Allawi told Iraq's interim national council.
"We will not be lenient."
But the BBC's Caroline Hawley in Baghdad says no one knows for sure where Zarqawi is.
And his capture, while it would perhaps end some of the most vicious attacks, would not put a stop to what is now a multi-faceted insurgency, she says.
Mr Allawi's call came as a group loyal to Zarqawi posted a video on the internet showing the beheading of two men it claims were members of the Iraqi government's
There was, however, some positive news regarding foreign hostages, with two the release of two Lebanese men seized last month west of Baghdad.