But that was apparently not immediately done, with a Pentagon spokesman saying five days later that he was unaware of any official requests "to participate in operations around Tikrit".
The issue of foreign air support, especially from the United States, is a point of contention between the Iraqi military and militiamen fighting alongside it.
Hadi al-Ameri, the commander of the powerful Iran-backed Badr militia, told journalists on Sunday that: "Some of the weaklings in the army... say we need the Americans, while we say we do not need the Americans."
The US faces a delicate balancing act in anti-IS efforts in Iraq, where working against the jihadists sometimes means taking part in operations that are also assisted by rival Iran, and involving militias that fought against American forces in past years.
Meanwhile the Canadian government said Tuesday that its air strikes against the Islamic State group in Iraq would be extended one year to March 2016 and may see sorties into Syria.
But no ground combat troops would be deployed under the plan, which is to be debated in parliament Thursday.