He told a news conference on Monday that he and Sadr had agreed on "the need to speed up the formation of a government that would group all the political movements and have a clear programme".
'Ready for concessions'
Meanwhile, Sadr told reporters that Allawi's bloc was "ready to make concessions to put an end to Iraq's political crisis". He urged other parties to do the same "for the sake of the Iraqi public interest".
"If there were past differences, I am forgetting them so that the political process proceeds," Sadr, who lives in self-imposed exile in Iran, said.
"I don't back specific names, but programmes and mechanisms to arrive at the next prime minister."
Bashar al-Assad, the president of Syria, also held talks with Allawi on Monday, in which he expressed his support for "any inter-Iraqi accord (on a government) which conserves the unity of Iraq, its Arab identity and its sovereignty," Syria's official Sana news agency reported.
Allawi in turn thanked Syria for hosting hundreds of thousands of Iraqi refugees and for its support for efforts to restore stability in Iraq.
Initial election results from Iraq showed Allawi's coalition taking a slim lead over the bloc of Nouri al-Maliki, the incumbent prime minister. But Allawi, a Shia, has been unable to form a coalition.
Al-Maliki, whose State of Law bloc trailed with 89 seats, has since joined with the National Iraqi Alliance to former a larger coalition but the new union still does not have enough seats to get a majority.
As the politician with the highest number of seats, Allawi believes his Sunni-dominated bloc should be able to form a government.
Allawi has said that failure to properly integrate Sunni's into the structures of power could reignite sectarian violence that killed tens of thousands.
Maliki's supporters say their candidate should stay on as prime minister because he represents the country's Shi'ite majority.