The one-two punch of Iranian-back militias and Iraqi government troops is likely to prevail in the unfolding battle for Tikrit, but it would not have been possible if U.S. airstrikes had not tied down Islamic State fighters elsewhere in northern Iraq, the top U.S. general said.

Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, was asked by reporters traveling with him from Washington to Iraq whether he believes the Islamic State group will be pushed out of Tikrit.

"Yeah, I do," he said. "The numbers are overwhelming."

Dempsey said about 23,000 Iranian-based Shiite militiamen and Iraqi soldiers are involved in the offensive, compared to only "hundreds" of IS fighters.

The offensive is not what the Americans would consider textbook military tactics, he said, describing a hodge-podge of Iraqi Humvees, trucks and other vehicles surging toward Tikrit like rush hour on the Washington Beltway.

"I wouldn't describe it as a sophisticated military maneuver," he said.

Dempsey was flying overnight Friday to Iraq to meet with U.S. commanders and Iraqi government leaders.

His visit comes at an intriguing stage of the war to force the Islamic State group out of Iraq. Its fighters swept across much of northern and western Iraq last summer and now control numerous key cities, including Tikrit, which is the birthplace of former Iraqi leader Saddam Hussein.

The U.S. and its allies have launched hundreds of airstrikes at IS targets since August and credits its attacks with halting the group's territorial advances. But in the Tikrit offensive, which began Monday, the U.S. is on the sidelines. It is watching as Iran asserts influence by providing training, weapons and leadership for Iraqi Shiite militias who are leading the charge on Tikrit.

Dempsey said he sees no evidence that the Iranian military is actually doing any of the fighting. They have improved the Iraqi militias' fighting capabilities, but their role also has raised worries among America's coalition allies, who include Gulf Arab nations who despise Iran.

Dempsey plans to visit one of those Gulf allies, Bahrain, during his trip.

The general said that while Iran is getting credit for enabling the Tikrit offensive, the full story of how it was made possible has not been told.

"If it weren't for the (U.S.-led coalition) air campaign over time depleting the ISIL forces in Beyji ... then the current campaign (in Tikrit) as currently constructed would not be militarily feasible," he said.

Islamic State forces had surged into Beyji, which lies just north of Tikrit, in hopes of controlling a key oil refinery there. But they have been halted and tied down by a series of U.S. airstrikes, Dempsey said. That little-noted IS setback has divided and weakened its forces, he added.

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

The mostly Sunni population of Tikrit must be allow to returned to their homes, and the Shiite-dominated government in Baghdad must step in with reconstruction and humanitarian aid, he said.

If that happens, "then I think we're in a really good place," he said. If it does not happen, then the future could be problematic, he said.

The key task for Iraq's leaders, Dempsey said, is to balance the Iranian role in empowering Shiite militias with Iraq's partnership with the U.S. and other coalition members.

"The only one that can balance that is the prime minister of Iraq," Dempsey said. "So I want to get his views on how he is seeking to balance that concern."