( CNN ) -- The Iraqi army shelled Falluja on Saturday in an effort to clear out al Qaeda-linked fighters amid dueling claims by the terror group and government forces about just who was in control of the flashpoint city in the Anbar province . The fighting in the Sunni province in recent days has posed a serious challenge to Prime Minister Nuri al-Maliki and his Shiite-dominated government , raising questions about his ability to hold the country together amid a rising insurgency . Conflicting reports have the Islamic State of Iraq and Syria ( ISIS ) , formerly the group commonly known as al Qaeda in Iraq , in partial control of Falluja , the site of some of the bloodiest fighting between U.S. forces and insurgents during the Iraq War . Al Qaeda on the rebound , experts say . The al Qaeda-backed group proclaimed it was in control of the heart of the city , with its flags planted on some government buildings and police stations , while two police officials and two tribal leaders told CNN that the vast majority of the city -- including government institutions and police stations -- was in the hands of Sunni tribesmen fighting alongside security forces . At least seven people were killed and another 31 were wounded in the shelling , according to medical officials at Falluja General Hospital . Fierce street-to-street fighting , between the insurgents and Sunni tribesmen aligned with police , also was reported in the provincial capital of Ramadi . Police say a number of casualties have been reported in the city , but did not offer a specific number . The al Qaeda militants in Ramadi warned al-Maliki and tribesmen to withdraw from the area or face violent consequences . In a video posted on YouTube , militants wearing masks warned al-Maliki 's supporters in Ramadi that they must stop helping `` al-Maliki commit crimes in Anbar or you will face harsh punishments . '' Al-Maliki has vowed to crush the insurgency in Anbar province , where the Sunni insurgency -- al Qaeda in Iraq -- flourished following the 2003 U.S.-led invasion that toppled Saddam Hussein . `` There will be no withdrawal , '' al-Maliki said in a speech Saturday carried by Al-Arabiya . Fresh fighting . Dozens have been killed and more than 100 wounded in fighting that broke out late last week following a raid on the home of prominent Sunni lawmaker Ahmed al-Alwani , a prominent supporter of anti-government protests . Al-Alwani 's brother and five of his bodyguards were killed during the raid , during which at least 16 other people were wounded , authorities said . That was quickly followed by a move to close two protest camps that were established last year as part of ongoing demonstrations against the Shiite-led government , which protesters have said has marginalized the country 's minority Sunni population . Since the withdrawal of U.S. troops in 2011 , Iraq 's minority Sunnis have become increasingly marginalized . They have accused al-Maliki of trying to consolidate power by carrying out mass arrests of Sunnis . Even so , a number of Sunni tribal leaders struck a deal with the government this week to fight alongside Iraq 's security forces against al Qaeda forces . The deal the government made with the Sunni tribal fighters was comparable to a 2007 U.S. pact that saw Sunnis turn on al Qaeda , siding with American and Iraqi forces to bring about an end to the terrorism . Violent flashback . The fighting between Sunni militants against Shiite-dominated forces was reminiscent of fighting during the height of the Iraq war in 2006 and 2007 , when sectarian violence nearly tore the country apart . State Department spokeswoman Marie Harf dismissed suggestions that the United States has abandoned Iraq following its withdrawal from the country in 2011 . `` Let 's be clear who 's responsible for the violence -- It 's the terrorists who were behind it , '' she told reporters in Washington on Friday . `` That 's why we are partnering with the Iraqi government very closely to fight this shared threat . At the end of the day , we can certainly help them fight it , but we also want to help them build their own capability to do so themselves . '' The United States is sending weapons , including Hellfire rockets and drones , to aid in the campaign against terrorism , officials have said . Harf said a number of American officials in Iraq and in Washington `` remain in touch with all of the different parties in Iraq . '' CNN 's Neda Farshbaf and Yousuf Basil contributed to this report .
NEW : At least seven people have been killed and 31 wounded in shelling , medical officials say . NEW : The Syrian government has said it will not negotiate with the rebels until they lay down their arms. NEW : ` ` There will be no withdrawal , '' Prime Minister Nuri al-Maliki says .