Tehran, Iran (CNN)The Basij is a militia made up of fighters loyal to Iran's religious leaders; their mission is to protect the country's Islamic order. To do that, they will go to any lengths necessary, including -- they say -- taking on ISIS. "We all are prepared to go and destroy ISIS totally," one Basij commander told CNN. "If our Imam, our Supreme Leader orders us, we will destroy ISIS." The commander says that, so far, the Basij has not been caught up in the fight against the feared Islamic extremists currently waging war in parts of Iraq and Syria. But Iran's elite Revolutionary Guard's Quds Force, led by General Qassem Suleimani, is already training, advising and supporting Iraqi Shia militias in their fight against ISIS. Suleimani was accused of involvement in the Shia insurgency against U.S. forces during the Iraq war. Today he is a celebrity to many Iraqis and Iranians. That is symbolic of the gulf that still exists between Iran and the U.S., regardless of any thaw in relations in the wake of the recent agreement on a framework nuclear deal and ongoing talks. Iran, militias' involvement in ISIS fight a mixed blessing . Iranian officials, who believe their strategy is making a difference in the fight against ISIS, say they would like better cooperation with the U.S., but point out that the level of trust simply isn't there. "At the moment, we consider the United States to be a threat to us because its policies and actions are threatening to us," said General Ahmad Reza Pourdastan, commander of Iran's ground forces. "We would like the US to change its rhetoric and tone of voice so that our nation could have more trust in U.S. military leadership." And the feeling is mutual: the U.S., which is leading the air campaign against ISIS in Iraq, has denied any direct coordination with Iran. Iran will do what it takes to fight ISIS . Iranians believe air strikes against ISIS are not effective, and feel that the U.S. and its allies are not trying seriously enough to defeat the group. Iran's President Hassan Rouhani told CNN's Christiane Amanpour last September that "the aerial bombardment campaign is mostly ... a form of theater, rather than a serious battle against terrorism." "The battle in Iraq is very important to Iran," explained Mohammed Marandi, a professor at Tehran University. "The Iranians believe that the Americans, if they wanted to, could do a lot more to put pressure on their allies. And also, if they were serious about air strikes, they could do a lot more." It's a point the U.S., of course, disagrees with -- U.S. President Barack Obama has vowed to "degrade and ultimately defeat" the terror group. But Iran remains unconvinced. "If they want to destroy ISIS, it is possible for them to achieve that," said Major-General Hassan Firouzabadi, Iran's chief of general staff. "The U.S. military and intelligence organizations have many ways to strike at ISIS, but we have not seen anything so far except intelligence gathering from the U.S. and Britain," he said. "We hope that one day, because of their national interests and the will of their nations, the U.S. and the UK will decide to really fight ISIS." In ISIS, Iran and the U.S. share a common enemy, but -- for now at least -- no apparent common strategy.Will Iran-Saudi proxy war erupt?
Iran's elite Quds Force is training, advising and supporting Iraqi Shia militias in their fight against ISIS.
Iranian officials say they would like better cooperation with the U.S., but say trust between the nations is lacking .