BAGHDAD, Iraq – Under heavy American pressure to end the crippling political stalemate, Iraq’s prime minister-designate yesterday proposed appointing a broad-based 36-member Cabinet – including a deputy premier from each of Iraq’s main Shiite, Sunni, and Kurdish factions.

But haggling continued over which individuals should fill the seats, adding to the worries of Iraqis, many of whom feel months of wrangling over the new government has emboldened insurgents to step up deadly attacks on American and Iraqi security forces.

Lawmakers allied with the premier said that in addition to the prime minister and three deputies, the Cabinet would have 17 Shiite Arab ministers, eight Kurds, six Sunni Arabs, and one Christian, fulfilling promises by leaders of the Shiite majority to share power among ethnic and religious groups. Officials said at least two ministers are women.

Prime Minister-designate al-Jaafari discussed his proposal with President Talabani yesterday, the premier’s spokesman, Abdul Razak al-Kadhimi, said. But some lawmakers later said the meeting didn’t take place. It was not possible to reconcile the conflicting reports.

Mr. Talabani’s three-member presidential council must sign off on the list before it is submitted to the 275-member National Assembly for a vote. Mr. Talabani already indicated he would not exercise his veto, and lawmakers said a vote could take place as soon as today.

However, such predictions have repeatedly proved false since Cabinet negotiations began after the parliamentary elections January 30.

Late yesterday, Mr. al-Jaafari went back for further talks with the head of the Supreme Council for the Islamic Revolution in Iraq, Abdel Aziz al-Hakim, and other members of his United Iraqi Alliance to discuss the candidates for the Cabinet, lawmakers said.

Alliance lawmaker Dhia al-Shakarchi said Shiite leaders raised concerns that some of the Sunni candidates might have had links to terrorist groups and to Saddam Hussein’s Baath Party, which brutally repressed Shiites and Kurds.

Under Mr.al-Jaafari’s proposal, Iraq’s Shiites would head 17 ministries, said Ali al-Adib and Hadi al-Ameri, lawmakers in the alliance, which holds 148 seats in parliament. Eight ministries would go to the alliance’s Kurdish allies, six to Sunni Arab groups, and one to a Christian faction, they said.