The US military's top officer said Friday Iran is bolstering the firepower of Shiite militias in Iraq but it remains unclear if Tehran is a help or a hindrance to the fight against Islamic State jihadists.

General Martin Dempsey, speaking to reporters aboard his plane en route to Bahrain and Iraq, said he would raise his concerns about Iran's influence in talks with Iraq's leaders --- days after Baghdad launched a large-scale operation to recapture Tikrit from the Islamic State group.

The Shiite militias, armed and advised by Iran, are playing a major role in the Tikrit offensive.

But the US-led coalition -- which has no dealings with the Shiite fighters -- has been markedly absent from the operation and allies fear Iran's activity could aggravate sectarian tensions.

Dempsey said US-led air strikes in recent months to the north near Baiji had put pressure on the IS extremists, laying the ground for the offensive on Tikrit.

"The Tikrit operation is only possible because of the air campaign we've been running around Baiji," where the IS was pushed away from oil refineries, Dempsey said.

"I want to make sure the prime minister and the minister of defense understand that and don't think this is all happening, you know, magically by the emergence of the Shia militia on the road . . . that runs from Baghdad to Tikrit," he said.

Referring to Iran's support for Shiite fighters, Dempsey said he is "trying to get a sense for how our activities and their activities are complementary."

He said that "we're alert to the challenges of having Iran supporting Shia militia," and Tehran's influence had sparked concerns in the anti-IS coalition, which includes Sunni Arab countries that view Iran as a threat.

It was not clear if Iran shared the same strategic goals as the Washington-led coalition, he said.

The international coalition was committed to a "unified" Iraq that represented the Sunni and Kurdish communities as well as the larger Shiite population, he said.

"I want to make sure that those efforts can truly be complementary. If they can't, we're going to have a problem, " he said.

- IS outnumbered in Tikrit -

Tehran has provided the Shiite militias with artillery, training, "some intelligence," overhead surveillance "of the kind they're capable of providing," he said.

But there was no sign that Iranian troops were directly "in the fight," he said, adding he would ask about that in his meetings in Iraq.

"One of the things that the Iranian influence does is it probably makes the Shia militia more militarily capable. Undoubtedly," the general said.

"But it also makes our coalition partners a little concerned."

Dempsey said "the only one that can balance that is the prime minister of Iraq," Haider al-Abadi.

"I want to get his views on how he is seeking to balance that concern."

He said it was only a matter of time before IS jihadists were defeated in Tikrit.

"The numbers are overwhelming," Dempsey said, adding that "hundreds" of IS fighters were facing an estimated 23,000 Iraqi army and Shiite militia troops.

It was the first time that the Iraqi army and Shiite militia "have been so intertwined in an operation," he said.

Columns of Iraqi military trucks and armored vehicles were lined up along the main road to Tikrit, and it resembled a rush hour traffic jam in Washington, "bumper to bumper," he said.

But he said the real test would come after the town is recaptured, and how the Iraqi government treats the mostly Sunni population in the area.

"The important thing about this operation in Tikrit is less about how the military aspect of it goes, and more about what follows," he said.

If Sunnis are allowed to return to their homes and "feel like the government is following an offensive with reconstruction and humanitarian assistance, then I think we're in a really good place," Dempsey said.

But if Sunnis are mistreated or forced out, and if the Baghdad government fails to deliver humanitarian aid, "then I think we've got a challenge in the campaign," he said.