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Mr. Alsalih said that in April when Iraq’s Sunni deputy prime minister, Rafi al-Eassawi, visited Tehran, the chief of Iran’s Quds Force, Qassem Suleimani, told the politician, “We already have 159 seats, what do we need you guys for?”

At the time, the two Shiite-dominated parties appeared close to forming a governing coalition, but that prospect has recently faded after Mr. Maliki insisted on remaining Iraq’s prime minister.

Mr. Kahl said Iran has overplayed its hand in Iraq.

“They tried to influence the provincial and national elections not very successfully,” he said. “They tried to defeat the U.S.-Iraq security agreement not very successfully. And I think that their experience with the militias that they’ve backed is that when they’ve overplayed their hands, they’ve gotten a lot of Iraqi pushback on this.”