KIRKUK, Iraq: Iraqi forces tried for a third day to close in on ISIS in Tikrit, as the top U.S. military officer said Iran’s role in the offensive could be positive, provided the battle did not become sectarian.

Around 30,000 security forces and allied fighters Monday launched the biggest anti-ISIS ground operation yet in Iraq, closing in on Tikrit from at least three directions.

A senior commander said operations were focused on cutting supply lines of weapons and reinforcements to the jihadis, who have held the city since June.

The next step will be to “surround the towns completely, suffocate them and then pounce on them,” Lt. Gen. Abdel-Amir al-Zaidi told AFP.

Troops have still not retaken Ad-Dawr to the south and Al-Alam to the north, but some units were already on the edge of the city, military sources said.

Zaidi said the operation had already secured areas further out in Salahuddin province and forcing ISIS fighters to regroup in urban areas.

“The first phase of the battle to liberate Salahuddin was successfully completed – and in record time – by clearing the areas in the east of the province,” he said.

The government advance has been slowed by car bombs, roadside bombs and sniper fire, as ISIS fighters retreated to urban positions but seemed unable to fight back in open areas.

Government forces, Shiite militias and volunteer units have been supported by Iraqi jets and helicopters, as well as Iran.

Prime Minister Haider al-Abadi said Sunday when he announced the Tikrit operation that residents should turn on ISIS.

Speaking to parliament the next day, he said that “in this battle, there is no neutral party,” arguing that anyone choosing neutrality was effectively siding with ISIS.

Many civilians fled the cities conquered by ISIS last year but the group has recently prevented residents from leaving in some recent cases.

A former army officer who gave his name as Abu Ahmad fled the town of Al-Alam with his wife and five children Sunday and said he had to pay a smuggler.

“We left with a ‘guide,’ a guy who knows the roads. We were five families, and paid him $1,000 each,” he said by telephone from Kirkuk.

The Kurdish-controlled city of Kirkuk is only 100 kilometers away but the route they took was a huge loop through the desert that saw them cover eight times that distance. “In the time it took us to get here, I could have gone to hajj and back,” he joked.Tikrit, a Sunni city 160 kilometers north of Baghdad on the Tigris River, is of both strategic and symbolic importance in Baghdad’s fight against ISIS.

It is the hometown of the late former President Saddam Hussein, the remnants of whose Baath Party have collaborated with ISIS. Commanders have also said Tikrit is a stepping stone toward a more ambitious operation of retaking second city Mosul to the north, which has been ISIS’ main Iraqi hub.

Iraqi Defense Minister Khaled al-Obeidi said Wednesday only Baghdad would decide the time and scale of an attack to recapture Mosul, after U.S. officials sent conflicting signals about the offensive.

A U.S. Central Command official said two weeks ago that the offensive could start in April or May, using 20,000 to 25,000 troops. U.S. officials have since suggested that timing could slip to the autumn.

U.S. Defense Secretary Ash Carter said Tuesday the original briefing was inaccurate and that military officials should not discuss war plans in any case.

“The liberation process will be purely Iraqi in terms of forces, timing, weapons and equipment,” Obeidi told a news conference in Baghdad alongside visiting Turkish counterpart Ismet Yilmaz.

“No one [else] has anything to do with it. This is our battle, the battle of the Iraqi army,” Obeidi said. “The role of the U.S.-led coalition is to provide air support, and this is agreed upon.”

General Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, told senators late Tuesday the battle for Tikrit represented the most open example of Iranian support for pro-government militias in Iraq.

“This is the most overt conduct of Iranian support,” Dempsey said, which came “in the form of artillery” and other aid.

“Frankly, it would only be a problem if it resulted in sectarianism,” he told the Senate Armed Services Committee.

U.S. commanders rarely discuss Iran’s activities in Iraq in public, stressing that Washington does not coordinate with Tehran’s military in any way – even though the two foes see ISIS as a common enemy.

U.S. officials have pressed the Shiite-led government in Baghdad to reach out to the country’s alienated Sunni community and worry that Shiite militia could persecute the Sunni community as they push to roll back ISIS.

If the Iraqi army and Shiite fighters “perform in a credible way” and defeat the jihadis in Tikrit, “then it will, in the main, have been a positive thing in terms of the counter-ISIL campaign,” Dempsey said, using an alternative acronym for ISIS.

Gen. Qassem Suleimani, head of Iran’s powerful Quds force, is reportedly on the ground with Shiite fighters coordinating the operation on Tikrit.