Al-Jaafari's Shia party, the United Iraqi Alliance (UIA), had made another attempt to save their embattled candidate by setting up a committee to talk to Sunni and Kurdish groups.
But Dhafir al-Ani, of the Sunni-led National Concord Front, said: "We have sent a letter to our Shia brothers explaining that our position remains the same - that of rejecting Prime Minister Ibrahim al-Jaafari's candidacy."
Mahmud Othman, a Kurdish member of the Iraqi parliament, said his group had again rejected al-Jaafari's candidacy.
Al-Jaafari has faced opposition from within the UIA, with Adel Abdel Mahdi, the Iraqi vice-president, saying he should resign.
"After we formally hear from the other lists, like the Iraqiya, which will also refuse to work with al-Jaafari, then we will today sit down in the alliance and decide," a senior UIA source said on Monday.
However, the group announced later in the day that it would postpone until Tuesday its decision whether to drop al-Jaafari.
Although the alliance has the largest number of seats in parliament, it falls short of an overall majority. Shia leaders need the Kurds and Sunnis to form a unity government.
Sunni and Kurdish groups accuse the prime minister of monopolising power and failing to lead the country adequately.
The US and Britain have urged al-Jaafari to step aside to break the deadlock over the formation of a government, believing that the political vacuum there is fuelling ongoing violence.
More than 100 Shias have been killed in a week during a series of bombings, some attacking religious sites.
Triple bombings killed 90 worshippers at a popular Baghdad mosque after Friday prayers, and 12 people died in a series of attacks on Sunday.