Gen. Qassim Suleimani, the head of Iran’s paramilitary Quds Force, has paid at least two visits to Iraq to help Iraqi military advisers plot strategy. And Iran has deployed about a dozen other Quds Force officers to advise Iraqi commanders, and help mobilize more than 2,000 Iraqi Shiite militia members from the country’s south, American officials said.

Iranian transport planes have also been making two daily flights of military equipment and supplies to Baghdad — 70 tons per flight — for Iraqi security forces.

“It’s a substantial amount,” said an American official, who declined to be identified because he was discussing classified reports. “It’s not necessarily heavy weaponry but it not just light arms and ammunition.”