The Pentagon insisted on Monday that said the U.S. strategy against the Islamic State in Iraq and Syria is working, despite the fall of a key Iraqi city.

"We still believe the strategy is working," Pentagon spokesman Army Col. Steve Warren told reporters.

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"Ramadi is an urban environment that is among the very toughest to fight in," Warren added in an acknowledgement that U.S. air power alone is no panacea for the city. "It is an environment that limits the ability of airpower, so it creates unique challenges," he said.

Warren said the Pentagon would accept help from Shia militia fighters — even though many are believed to be backed by Iran — to retake the city.

"The militias have a part to play in this. As long as they are controlled by the central Iraqi government, then they will participate," Warren said.

Warren expressed confidence that the coalition would be able to retake Ramadi from ISIS, but did not lay out any clear steps or a timeline.

"We will take Ramadi," he said. "We will retake it in the same way that we are slowly but surely retaking other parts of Iraq and that is with Iraqi ground forces, combined with coalition airpower.

"I'm not going to put a timeline on it. This is an Iraqi decision, as with every other city in ISIL control, it has to be done on Iraqi timelines," he said.

Republican and Democratic lawmakers on Monday blasted the decision to allow Shia militia fighters to help, arguing it would increase sectarian tension in Anbar, which is dominated by Sunnis.

“Whatever operational success Shia militias may have in Anbar would be far exceeded by the strategic damage caused by their violent sectarianism and the fear and suspicion it breeds among Iraqi Sunnis,” said a statement by Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.).

Rep. Adam Schiff (D-Calif.), the House intelligence committee's top Democrat, also said sending in Iranian-backed Shia militias would "only make the sectarian problem in the region worse."

McCain called for more U.S. trainers on the ground in Iraq. They currently number about 3,030.

But Warren pushed back against the idea that U.S. forces were needed on the ground to defeat ISIS. He said so far, the coalition has trained 7,000 Iraqi Security Forces, and has about 3,000 to 4,000 more forces to train.

Lawmakers have also called on the administration and for Baghdad to do more to support Sunni fighters.

“Defeating ISIL requires empowering Sunnis who want to rise up and fight ISIL themselves, including by integrating them into Iraq’s security forces and providing more robust American military assistance,” McCain and Graham said.

“All efforts must be made to step up the pace of arming Sunni tribes willing to fight ISIS and reclaim their towns, and to integrate such forces within the Iraqi military,” added Schiff. “The war in Anbar will not be won until the Sunni tribes feel they can protect themselves — from ISIS and the threat of militia abuses."

The House National Defense Authorization Act orders the defense secretary to certify that the government is fairly distributing military aid to the Sunni and peshmerga fighters. If not, military assistance would be provided directly to Sunnis and peshmerga.

The White House has objected to those provisions, and Warren said the Pentagon still planned to flow weapons through Baghdad for distribution to Sunni and peshmerga fighters.

"We're going to stick with our policy because we believe that by flowing resupply directly to the Iraqi central government and allowing the Iraqi government to then resupply outlying areas that will help generate a more centralized, unified, Iraqi government," he said.