The Iraqi Shiite Coordination Framework alliance on Monday said it still will stick to the nomination of Mohammed Shia al-Sudani for prime minister.
In a statement, the framework, a coalition of groups close to Iran, confirmed that it had not discussed the nomination of another candidate.
It added that it had reached "advanced understandings" with Iraqi groups and continues dialogue with all parties to meet "the constitutional deadlines."
The al-Sadr movement, which has 73 members in Iraq's 329-seat parliament, sought to form a government of national majority but was hindered by the framework group.
Amid this political deadlock, MPs loyal to Muqtada al-Sadr resigned in June, causing further political tension in Iraq.
Tension has been running high across Iraq in recent weeks as rival Iraqi groups failed to agree on a new prime minister since the country's elections last October.
More than 30 protesters were killed last week when supporters of al-Sadr stormed Baghdad's Republican Palace, the seat of the government, after the firebrand leader said he was stepping down from politics.
