The State of Law bloc of Nouri al-Maliki, the incumbent prime minister, trailed with 89 seats. He has 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.
In a speech to Iraqi leaders on Sunday, Biden said that "subordinating individual interest is fundamental to the success of any nation", as mortars landed in the heavily fortified Green Zone where the US embassy is based.
"Iraqiya, State of Law, Iraqi National Alliance, the Kurdistan Alliance all are going to have to play a meaningful role in this new government for it to work," Biden said, adding that the US has no "hidden agenda" in the trying to shape a power sharing deal.
US combat troops are due to leave the country by September 1, although an advisory and training force of 50,000 will stay behind until December 2011.
"We are not disengaging from Iraq, our engagement is changing," he said.
Moqtadr al-Sadr, the influential Shia leader, some of whose supporters are in the Iraqi National Alliance, said that Iraqi politicians should not co-operate with Biden or other US officials.
"I advise Allawi and Maliki not to allow the occupier to intervene," Sadr said in a statement.
As the politician with the highest number of seats, Allawi believes his Sunni-dominated 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.
A suicide attack outside of government offices in Anbar province on Sunday killed at least four people and wounded 23.
Maliki's supporters say their candidate should stay on as prime minister because he represents the country's Shi'ite majority.
There are currently 75,000 US troops in Iraq and, according to an aide to Maliki, Biden is worried that the political impasse will create a security vacuum and re-inflame sectarian tensions.