On Wednesday, Iraqi President Jalal Talabani held a round of meetings with Kurdish, Sunni, and Sadrist politicians in a resort in Iraq's autonomous northern Kurdistan region to hear their demands.
"They could not persuade the president to send a message to parliament to hold a vote of no confidence," Kurdish lawmaker Mahmud Othman said. He said Talabani prefers to convene talks among all coalition members to resolve their differences.
Talabani later issued a vague statement, saying he remained committed to the constitution.
Even if a no-confidence vote is held, it is not clear that Maliki's opponents could muster the needed absolute majority, or 163 of parliament's 325 members, to bring down the government.
Earlier Wednesday, two senior politicians said Iraq's powerful Shiite neighbor, Iran, had stepped up efforts to protect Maliki.
"There is some Iranian pressure on the president not to send the letter to parliament and to support Maliki," said a lawmaker of Maliki's political bloc, speaking on condition of anonymity because he was not permitted to discuss sensitive political dealings with reporters.
Talabani is a Kurd but has close ties to Iran.
A senior Sadrist said Maliki was still seen by the movement as the best option, despite growing concerns that he is amassing power.