When the United States said this week that American forces in Iraq faced threats from Iranian “proxies,” it was referring to the armed groups that helped fight the Islamic State and have bedeviled Iraq ever since.

The Iraqi armed groups, some with ties to Iran, have a footprint in every Iraqi province. Whether they function as Iranian proxies, however, is far from settled.

“The word ‘proxy’ implies that these are tools of Iran, and they aren’t,” said Anthony H. Cordesman, a national security analyst at the Center for Strategic and International Studies.

“You have a range of groups in Iraq’s Popular Mobilization: Some are Sunni, some are pro-Iraqi government, some have ties to the Quds force and the Islamic Guard,” he said.