Saleh Mutlak, an outspoken Sunni lawmaker, said Shiite lawmakers should instead focus on the country's fragile economy and security.
A prominent Shiite legislator, Shatha al-Mousawi, said she and other Shiite lawmakers met with him recently in his home to try to resolve an issue within the Shiite bloc.
He blamed several Shiite lawmakers loyal to the cleric Moktada al-Sadr for accusing Mr. Dulaimi of taking part in sectarian killings.
"Things were predictable," said Ali al-Adeeb, a prominent Shiite lawmaker who was just finishing lunch in the dining area of the Parliament building.
"Most of his problems are with the Sadrists," said Jalal al-Din al-Sagheer, a Shiite lawmaker from a rival party.
A1 Iraq's leading political blocs agreed to remove the speaker of Parliament from his position after accusations that his bodyguards assaulted a Shiite lawmaker as the speaker cursed him.
"They told us, please don't discuss this or make objections, just vote for the statement," Shatha al-Musawi, a Shiite lawmaker, said of the Shiite leadership.
They will be codified in a memorandum between Prime Minister Nuri Kamal al-Maliki and President Bush, Shiite lawmakers said, although the type of document is still a subject of debate.
It was not clear what led to the breakthrough in the talks, but some Shiite lawmakers seemed supportive of the agreement.
Ayatollah Sistani's support of the constitution, which was written largely by Shiite lawmakers, is not surprising, but the wording described for the fatwa is more direct than was anticipated and suggests he could have concerns that it will not pass on its own.