He acknowledged there were current problems in his country, especially in the violence-wracked city of Falluja, but these would not prevent the elections from being held.
In an interview published on Monday in several western newspapers, Allawi said: "If for any reason 300,000 people cannot have an election, cannot vote because terrorists decide so, then frankly 300,000 people ... is not going to alter 25 million people voting."
If the elections were prevented in Falluja, its inhabitants could vote later, the prime minister said.
His government was "determined to win the war against the terrorists, and establish democracy in Iraq", Allawi told Le Figaro.
He also expected ousted Iraqi president Saddam Hussein to go on trial before the end of the year and hoped the trial would help establish a clear distinction between members of Saddam's Baath party who committed crimes during his rule, and those who simply joined the party because they had to.
Of former Baath party officials who did not commit crimes, he said: "We are not interested in pursuing them. They should be part of the civil society of Iraq, part of the political process."
Saddam Hussein is expected to go
on trial before the end of 2004
Meanwhile, US Secretary of State Colin Powell said on Sunday the United States was confident elections could be held in Iraq on schedule in January despite the unrest raging in the country.
"There is an insurgency raging. We see it every day, there's no question about it."
Asked if elections could be held in one part of the country but not another, Powell said: "I'm not saying that ... our strategy is to bring all these places under government control and to do it in time for the elections."
More than 100 people died in a wave of bombings and battles between US troops and armed fighters in Iraq on Sunday.