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BBC MUNDO RADIO
Iraq election: Iyad Allawi's bloc wins most seats
The BBC's Andrew North on "an incredible upset"
His coalition has two seats more than that of incumbent PM Nouri Maliki, who has vowed to challenge the results and said they were "not final".
Earlier, the UN's envoy to Iraq said the 7 March election was "credible" and urged Iraqis to accept the results.
Mr Allawi will need to form a coalition government as he lacks a majority, amid fears the results may spark violence.
Just hours before the results were announced, twin bomb blasts in the town of Khalis, in Diyala province, killed at least 40 people and left more than 60 injured.
Speaking directly after the figures released by the electoral commission, Mr Maliki challenged the result and repeated his call for the electoral commission to recount the vote.
He added that his bloc would press ahead with plans to form the new government.
Mr Allawi said his bloc would "work with all Iraqi parties, whether they won or not, to form the next government".
The BBC's Andrew North in Baghdad says this looks like a spectacular victory for Mr Allawi and a big upset for Mr Maliki - but at 91 seats to 89 it was a very tight race.
And with Mr Maliki's party making allegations of irregularities, there are still concerns over whether theresult will be accepted, our correspondent says.
On Thursday the head of Iraq's election commission ruled out holding a manual recount of all the votes cast.
The US state department congratulated the country on carrying out "a successful election". Spokesman Philip Crowley said Iraqi and international observers had overseen the process and there was "no evidence of widespread or serious fraud".
"This marks a significant milestone in the ongoing democratic development of Iraq," he said.
A credible election is seen as crucial to US military plans to end combat operations this August, seven years after the invasion.
