The US-approved interim PM also said his government would extend across the country an arms-for-cash programme that started last week in the Baghdad suburb of Sadr City, in a bid to rid the streets of weapons ahead of planned January elections.
"We will open this disarmament initiative to all the cities in the country, we will start with Basra," Iraq's second city in the south, Allawi said in a speech to the interim Iraqi parliament.
Meanwhile, the International Committee of the Red Cross (ICRC) said on Monday it had sent 1.5 tonnes of urgent medical and surgical equipment to a hospital in Falluja.
"The aid was transported by two ambulances from the regional health department," the Geneva-based agency said in a statement.
Humanitarian aid - 1500 food parcels and 1000 water containers - had also been distributed by lorry to families who have fled the beseiged to nearby towns such as Habbaniya, Aamriya or Saklawiya.
The ICRC "expresses its deep concern over the mounting violence in the town of Falluja. The committee calls on both sides to allow the wounded to receive treatment at hospital."
Falluja, 50km west of Baghdad, has been the target of almost nightly US air strikes in recent weeks as US and Iraqi forces seek to end control of the city and hunt down Abu Mussab al-Zarqawi - the country's most sought after man who they claim to be in the city.
In a separate development, Macedonian officials said they were investigating a purported Iraqi group's reported claims to have executed two Macedonians for allegedly spying for US forces in Iraq.
The aid organisation said it had
sent 1.5 tonnes of supplies
"For now we only have some details about that event in Iraq but we don't have confirmation and we don't know if it's true," interior ministry spokesman Goran Pavlovski told reporters on Monday.
"We are contacting the authorities in Iraq to find out what this is all about. We are checking all information."
Aljazeera earlier reported that an armed group calling itself the Islamic Army in Iraq had claimed responsibility for executing two unnamed Macedonians.