That could doom Mr. Maliki's plan, said Ayad Jamaladin, a moderate Shiite legislator on the government's reconciliation committee.
"This strategy will destroy their goal of establishing democracy in Iraq," said Abbas al-Bayati, a prominent Shiite legislator.
A Shiite legislator, Sami al-Askari, said a deal was struck to delay debate until next week to allow Parliament to examine constitutional changes sought by Sunnis.
A look of relief seemed to pass over Mr. Maliki's face, said Sami al-Askari, a conservative Shiite legislator who was in the room.
"I think it's a leap into the unknown," said Sami al-Askari, a Shiite legislator who advises Mr. Maliki.
"There is a real trust crisis," said Baha al-Aaraji, a prominent Shiite legislator at a news conference broadcast on television.
On Monday, Shiite legislators circulated a draft proposal expressing their suspicions about the motives for Mr. Moussa's visit.
During a session of Parliament last week, prominent Sunni and Shiite legislators bitterly accused each other of sectarianism and promoting violence.
"Many in the Shiite and Kurdish alliance have fears, because they suffered oppression in the past," said Adel al-Amari, a Shiite legislator.
"He didn't transfer real power to the Iraqis," said Hassan al-Sineid, a Shiite legislator and adviser to Mr. Maliki.