Figures within Iraq's majority Shia alliance have for the first time urged Ibrahim Jaafari to stand down as PM to help a national unity government form.
Mr Jaafari has failed to gain Sunni and Kurdish support
Key alliance politician Qassim Daoud made the call, saying it would help break the political deadlock.
Mr Jaafari, a Shia, is opposed by the minority Sunni and Kurdish blocks.
Senior Shia figures said this week the US ambassador to Iraq had told them the US did not want Mr Jaafari to stay. Mr Jaafari warned the US not to interfere.
A key aide to Mr Jaafari told Reuters news agency on Saturday the prime minister would not give in to the calls to resign.
Jawad al-Maliki said Mr Jaafari would go on "until the end".
Mr Daoud leads an independent bloc within the United Iraqi Alliance.
He said: "I call on Jaafari to take a courageous step and set a fine example by stepping down.
"There is a current [within the alliance] that is calling on the prime minister to withdraw his nomination because the political process has reached a deadlock."
Saad Jawad Qandil, of the Supreme Council for Islamic Revolution in Iraq, a key alliance party, said there had been "numerous calls" by individuals to change Mr Jaafari "to resolve the ongoing political crisis".
Mr Jaafari was chosen by the ruling Shia-led bloc after it won December's election.
But Kurdish and Sunni Arab parties have rejected the nomination and have threatened to boycott a national unity government unless Mr Jaafari withdraws.
The delay in forming a government is thought to be partly responsible for fuelling the increasing sectarian violence which has struck Iraq since last month's bombing of a key Shia shrine at Samarra.
Other sources within the alliance said as many four of the blocs within the grouping wanted Mr Jaafari to stand down if he could not gain Sunni and Kurdish support.
"Daoud's call is supported by at least 60% of alliance members of parliament," a senior alliance official told Reuters.
The Shias control 130 seats in the 275-member parliament.
This week senior Shia politicians said US ambassador to Iraq, Zalmay Khalilzad, had told them President George W Bush "doesn't want, doesn't support, doesn't accept" the retention of Mr Jaafari.
Mr Jaafari responded by saying the comments undermined Mr Bush's commitment to democracy in Iraq.