Qassem Soleimani, Iran's top officer responsible for foreign operations, provides assistance in Iraq "whenever we need him," Hadi al-Ameri, the commander of the Badr militia, said on Sunday.

"He was giving very good advice. The battle ended now, and he returned to his operations headquarters," Ameri told journalists close to the Al-Alam area north of Baghdad.

He was apparently referring to the battle to retake the nearby city of Tikrit from the Islamic State (IS) jihadist group, which began earlier this month and has since become a siege.

"Qassem Soleimani is here whenever we need him," said Ameri, whose Badr militia is a powerful Iranian-backed force in the fight against IS.

Ameri's remarks are a sign of the important role Soleimani plays in military operations against IS in Iraq and the influence Tehran wields here, both much to Washington's chagrin.

Soleimani has advised Iraqi forces in multiple operations against IS, which led a major offensive last June that overran large areas north and west of Baghdad.

In doing so, he and other Iranian advisers provide the kind of forward support during operations that US President Barack Obama has yet to authorise American forces to undertake.

Soleimani has played an increasingly public and open role in the fight against IS, a major change for a man who was once known as the elusive operative leading Iranian efforts against the US in Iraq.

Now, his face is widely known, pictures of him are shared on social media, and he has even been the topic of music videos.