The leader of the secular alliance that narrowly won this month's poll told the BBC that Tehran was interfering directly in Iraq's electoral process.
His Iraqiyya bloc beat the rival State of Law alliance of Prime Minister Nouri Maliki by just two seats.
Both the UN and US envoys to Iraq have said the 7 March poll was credible.
But Mr Maliki has said he will challenge the count through the courts.
Despite winning the election, Mr Allawi is a long way short of the majority he needs to form a government, says the BBC's Andrew North in Baghdad.
Much of his support came from Iraq's Sunni minority, our correspondent adds, but most of the parties he would need to back him represent Iraq's Shia majority, and have close ties to Iran.
Difficulty governing?
In an interview with the BBC, Mr Allawi said it was "very clear" that Iran was trying to stop him from becoming prime minister.
"Iran is interfering quite heavily and this is worrying," he said.
He accused the Iranian government of interfering by inviting all the major parties to Tehran for talks, except his own Iraqiyya bloc.
"They have invited everybody – but they haven't invited us – to Tehran," he said.
He said he was concerned Tehran was also influencing a commission that has been vetting candidates for ties to Saddam Hussein's Baath party, which may disqualify more of his supporters.
Some are likely to see Mr Allawi's comments as an excuse for the possibility he may not be able to form a government, says our correspondent.
While many Shias backed him, others are suspicious of his past links to the Baath party.
The Iranian embassy in Baghdad declined to comment.
'Largest bloc'
According to final results published by Iraq's Independent High Electoral Commission (IHEC), Mr Allawi's secular Iraqiyya bloc won 91 of the Council of Representative's 325 seats, 72 short of a majority.
Mr Maliki's State of Law came second with 89 seats, followed by the Iraqi National Alliance (INA) on 70, and the Kurdistan Alliance with 43.
Iraqiyya's narrow victory means Mr Allawi, a Shia, will be given the first opportunity to form a coalition government.
If he fails to do so within 30 days, Iraq's president will ask the leader of another bloc.
There is concern that a challenge to the election result could be lengthy and divisive, endangering progress towards greater stability.
Sectarian violence erupted in 2005 as politicians took months to form a government after the last parliamentary election.
