As the 275-member parliament convened on Sunday, Bahaa al-Araji, a member loyal to the anti-American Shia figure Muqtada al-Sadr, denounced what he said was continued US meddling in the selection of ministers for the coveted interior and defence ministry posts.
He set a deadline of two days before the 130 alliance deputies act unilaterally.
"Within the past two days, the occupation forces have been interfering with certain names and certain posts," al-Araji said. Al-Araji's group holds 30 seats in parliament.
"There are also blocs participating in the [formation of] the government that have begun demanding more than what they are entitled to electorally.
"We have set a limit of within two days, and the blocs should abide by this timeframe and act in accordance with the rules upon which we have agreed. Otherwise, we will form a government without regard to their demands."
Sunni deputies issued their own threats, with one member of the three-party Sunni Arab coalition that holds 44 seats in parliament threatening to walk out of the talks and the government.
Salman al-Jumali said: "If we do not get what we deserve, we will end our participation in the political process.
"Our representatives in parliament, and the officials already awarded ministerial posts will withdraw."
Al-Jumali said they wanted the defence, education, planning and health ministries, as well as some ministries of state.
The new warnings came as a May 22 constitutional deadline for Nuri al-Maliki, the prime minister-designate, to form a government approached.
Al-Maliki has a May 22 deadline
to form a government
Earlier, another member of the United Iraqi Alliance, the Fadhila party, rebuffed a call by al-Maliki to return to the cabinet formation negotiations, saying the political process was tainted and that the incoming government will be little more than an amalgam of personalities out of tune with the needs of Iraqis.
Deputies have said that without unanimity on key posts, al-Maliki may announce a partial cabinet and temporarily retain control of the interior and defence ministries until suitable candidates are agreed upon.
Meanwhile, leading negotiators said that nuclear scientist Husain al-Shahristani, a Shia politician once jailed by Saddam Hussein, the former president, seems increasingly likely to be Iraq's next oil minister.
"We are now 80% sure that this job will go to Shahristani," one senior negotiator said, adding that only a surprise development could now block his appointment.
Three senior officials from the United Alliance, the Shia bloc to which both Shahristani and al-Maliki belong, agreed Shahristani would probably get the job but he still faced objections from some parties within the alliance.