The process, a complicated task of political jockeying that took months the last time around, was given new urgency by the Sunni militant campaign launched last month that has swallowed parts of Iraq and brought the country to the brink of disintegration.

Ayatollah Sistani took the unusual step of sending a letter directly to Mr. Maliki’s office last week that made clear the cleric’s opposition to a third term, a message also made clear to the visiting Iranian officials, said three Iraqi politicians involved in the talks.

Mr. Sistani’s letter was a sign that he believes the prime minister has become divisive even within his own Shiite support base and is unable to lead the country out of the latest crisis, several Shiite politicians said.