Two car bombs in Iraq are feared to have killed 23 people, all civilians, the US military has said.
Allawi has vowed to crush the insurgents
The explosions went off near a mosque in the town of Hilla - until now relatively calm - on Saturday evening.
Meanwhile, doubt has now been cast on an apparent warning by Iraq's interim prime minister that January's elections could be delayed if violence continued.
Iyad Allawi said his remarks had been "misinterpreted" and that elections would take place by 31 January 2005.
He also said he plans to offer amnesty to those who resisted the US occupation "out of desperation".
Writing in the UK's Independent on Sunday newspaper, Mr Allawi said his government's priority would be to establish security, which was a condition of progress.
Throughout this process, his government would make "a clear distinction between those Iraqis who have acted against the occupation out of a sense of desperation, and those foreign terrorist fundamentalists and criminals whose sole objective is to kill and maim innocent people and to see Iraq fail."
He went on: "Plans are being drawn up to provide amnesty to Iraqis who supported the so-called resistance without committing crimes, while isolating the hardcore elements of terrorists and criminals."
Mr Allawi has stressed that free and fair elections are vital, but in an interview with the US' CBS News, he appeared to suggest continuing violence could delay polls.
"We are committed to elections and one of the tasks is really to work toward achieving these objectives. However, security will be main feature of whether we will be able to do it in January, February or March," he told the network.
But he later told reporters "we will do it by 31 January", saying of the CBS report: "That was a great misinterpretation, it was taken out of context."
White House spokesman Scott McClellan said Washington remained "committed to that [elections by January], but we also understand the concerns that the prime minister is raising about the security situation".
The US-led coalition is due to hand over power to Iraq's interim government on 30 June and the Iraqis are then expected to facilitate United Nations-backed general elections.
While Iraqi leaders contemplate ways to establish security, the violence has continued unabated.
Iraq's leaders are considering imposing emergency laws
Suspected al-Qaeda-linked gunmen say they have taken three Turks hostage and are threatening to kill them if Turkish firms do not withdraw from Iraq by Tuesday.
They also called on Turks to protest during the Nato summit taking place in Istanbul, at which President Bush is set to seek the alliance's help in stabilising Iraq.
More than 100 Iraqis have been killed over the past week, with most of the attacks aimed at Iraq's security forces and other people working with the coalition authorities.
But there appear to have been no such targets in Hilla, a town about 100km (60 miles) south of Baghdad, where Saturday evening's blasts happened near a mosque on a busy street.
Hospital sources in Hilla said 23 people had been confirmed dead, with 58 injured. The US military initially said that up to 40 people had died, but have now issued a statement that also puts the number killed in Hilla at 23.