Talabani told reporters after meeting Zalmay Khalilzad, the US envoy, on Sunday: "I stressed to the American ambassador on the necessity of forming a national unity government in which no one will be excluded, especially [Allawi's] Iraqi [National] List.
"The Iraqi List has to take part in the coming government. The Kurdish Coalition will not take part in the coming government unless the Iraqi List takes part in it."
Allawi, a secular Shia who enjoys US support, has been touted for a key cabinet portfolio, possibly the interior ministry, which controls Iraq's security forces.
His bloc won only 25 of parliament's 275 seats in the polls on 15 December.
But leaders of the Shia coalition that won the largest number of seats in the parliament and will lead the next government have voiced strong opposition to Allawi claiming a prominent portfolio.
"There are parties [setting] red lines about the participation of the Iraqi List [in the next government], but these red lines are red for us too," Talabani said.
"Any rejection of the Iraqi List is a rejection of the Kurdish Coalition"
Jalal Talabani, the president of Iraq
"Any rejection of the Iraqi List is a rejection of the Kurdish Coalition."
Support of the Kurdish Coalition, which has 53 seats, is vital for any bloc wanting to form the next government.
Sunni Arab leaders have voiced opposition to religious Shia leaders claiming the interior and defence ministry portfolios, which would give them control over the police and armed forces.
Talabani and Allawi are secular-minded politicians who led opposition to Saddam Hussein's regime, before it was toppled in the US-led invasion of 2003.
The Kurdish Coalition was a key member of the outgoing government, but Talabani has also complained about Kurds not receiving key ministries and alleged Shia security force abuses against Sunni Arabs.