"I call on Jaafari to take a courageous step and set a fine example by stepping down," said Kasim Daoud, a senior member of the independent group within the Alliance.
A senior aide to al-Jaafari responded by saying the Iraqi prime minister would not step aside and give up his nomination for a second term in office.
"He is definitely not going to step down. He is the only candidate and will continue to the end," said Jawad al-Maliki, a senior official in al-Jaafari's Dawa party.
Other senior Alliance officials confirmed that four of seven main groups within the bloc wanted al-Jaafari to give up the nomination if, as is likely, he fails to persuade Sunni and Kurdish parties to drop their refusal to serve in a cabinet under him.
"There is a broad trend inside the alliance who want Jaafari to do this [step aside] and we expect him to do so," Daoud said.
"We have stood behind him for 50 days and today we have reached the conclusion that there should be a prime minister for all Iraqis, not just one group."
Alliance officials said seven key groups inside the bloc had concluded by a four to three majority to give al-Jaafari just days to persuade the Kurds, Sunnis and secular leaders to drop their opposition to him.
Minority groups within the alliance have formally written this week to leader Abdul Aziz al-Hakim urging him to produce a more acceptable candidate.
Hakim's SCIRI party and its Badr allies, the independents and the Fadhila party voted against al-Jaafari.
The Iraqi prime minister continues to have the support of his own Dawa party, its Dawa-Iraq allies and the movement of Muqtada al-Sadr, the Iranian-backed cleric and militia leader.
He beat a candidate from Hakim's SCIRI party by a single vote in an internal ballot in February.
It was not clear what mechanism might be used to choose a new nominee for prime minister nor who that might be.
A favourite may be Adel Abdul Mahdi, the vice-president and defeated SCIRI candidate.