BAGHDAD (Reuters) - A prominent Iraqi militia indicated on Thursday it would give any heavy weapons it had to the military once Islamic State was defeated and rejected a proposed U.S. congressional bill designating it a terrorist group. Harakat Hezbollah al Nujaba, which has about 10,000 fighters, is one of the most important militias in Iraq. Though made up of Iraqis, it is loyal to Iran and is helping Tehran create a supply route through Iraq to Damascus. The Nujaba fights under the umbrella of the Popular Mobilization Forces (PMF), a mostly Iranian-backed coalition of Shi ite militias that played a role in combating Islamic State. Disarming the PMF is seen as Prime Minister Haider al-Abadi s most difficult test as Iraqi forces edge closer to declaring victory over the Sunni militants.  The heavy weapons belong to the Iraqi government, not us. We are not rebels or agents of chaos and we do not want to be a state within a state,  Hashim al-Mouasawi, the group s spokesman, said at a news conference on Thursday. He was responding to a Reuters question on whether his group would obey orders by Abadi, who as prime minister commands the military, to return heavy weaponry, reduce the number of fighters, or withdraw from Syria. He would not be drawn on the reduction of fighters or Syria.  The PMF is under the command of the Commander-in-Chief of the Armed Forces and naturally when the war is over and victory is declared, the final decision will be his,  Mouasawi said. His comments broadly echoed those of Iraqi military spokesman Brigadier General Yahya Rasool.  The tanks, armored vehicles, and machine guns belong to the army and it is natural that after the battles are over they return to the army,  Rasool told Reuters in an interview. Nujaba strongly objected to moves by Washington towards designating it a terrorist group. Nujaba blames the United States, without providing evidence, for the creation of IS. Republican U.S. Representative Ted Poe introduced a bill this month to the House of Representatives that would place Nujaba and another militia loyal to Iran on a list of terrorist groups and give President Donald Trump 90 days to impose sanctions on it once it passed.  The bill was referred to the House Committee on Foreign Affairs, sparking condemnation in Baghdad from Iraqi lawmakers and Abadi himself, who said he would not allow anyone who fought Islamic State to be treated as criminals.  Accusing us of terrorism is not new or surprising. It is not a coincidence, and does not shock us, because we have never been part of the American bloc or project,  said Mouasawi. Iraq is backed by adversaries the United States and Iran in its fight against Islamic State. The United States is concerned that Iran, a Shi ite Muslim regional power, will take advantage of gains against Islamic State in Iraq and Syria to expand the influence it amassed after the U.S. invasion in 2003, something Sunni Arab rivals such as Saudi Arabia also oppose. Tens of thousands of Iraqis heeded a call to arms in 2014 after Islamic State seized a third of the country s territory, forming the PMF, which receive funding and training from Tehran and have been declared part of the Iraqi security apparatus. They are paid by the Iraqi government and officially report to the prime minister, but some Arab Sunni and Kurdish politicians describe these militias as a de facto branch of the Iran s Islamic Revolutionary Guards Corp (IRGC). Mouasawi openly said on Thursday his group receives support in the form of  advice  from the Guards and the commander of its foreign operations, Major-General Qassem Soleimani, and Lebanese Shi ite political and military group Hezbollah. 