Leaders from the United Iraqi Alliance (UIA) met for about two hours on Tuesday but failed to decide on whether or not to replace al-Jaafari after his candidacy faced stiff opposition from the Kurdish and Sunni factions.
They broke off talks intended at resolving Iraq's political impasse until Wednesday.
Bassim Sharif, spokesman of the Fadhila party, one of the members of the Shia alliance, said: "The meeting has ended. The leaders will meet again Wednesday."
Sharif said the Shia leaders heard the report of a three-member committee that was mandated by the alliance to hold talks with the Kurdish, Sunni and the secularist groups over al-Jaafari's candidacy.
"Their report was heard," he said, adding that the secularists led by Iyad Allawi, the former prime minister, "had reservations about the programmes of the alliance and not about al-Jaafari himself".
On Monday, Allawi's group, along with the Kurds and the Sunni Arabs, had rejected al-Jaafari's candidacy.
Earlier on Tuesday the Fadhila party stepped up pressure on the alliance by saying it was ready to offer a candidate to replace al-Jaafari if the Shia alliance failed to pass his candidacy.
"If the UIA does not succeed in securing the candidacy of Mr al-Jaafari, the Fadhila party is ready to propose another candidate," Sharif said, without giving a name.