AP -- Nearly every night for a year, mortar and sniper fire from Islamic State group militants has pinned down outgunned Iraqi troops on the edge of Fallujah.
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The city, the first to fall to the Sunni extremists a year ago this month, exemplifies the lack of progress in Iraq's war against the Islamic State group, which holds a third of the country. U.S.-led airstrikes and Iranian aid have helped Iraqi troops, militiamen and Kurdish fighters take back bits around Islamic State-held territory, but recapturing it all remains far out of reach.
"We are constantly on alert and don't sleep very much," said Saad al-Sudani, an Iraqi soldier among the beleaguered troops outside of Fallujah. "We are waiting for any kind of support."
The fall of Fallujah in January 2014 started the Islamic State group's dramatic blitz across Iraq. In June, the extremists captured Iraq's second-largest city, Mosul, then swept south toward Baghdad in a march that put almost all the Sunni-majority regions of northern and western Iraq into its hands. The Iraqi military crumbled, with troops often dropping their weapons and fleeing.
A year later, the extremists still rule Fallujah, which saw some of the heaviest fighting of the U.S.-led war of 2003.
General John Allen, the U.S. envoy to the anti-Islamic State coalition, said that advise-and-assist teams are working to train and equip 12 Iraqi brigades to prepare them for retaking Fallujah and Mosul.
"We expect that we'll see the effectiveness of this force improve over time and ultimately that they'll be able to take back the population centers and the municipalities," Allen told journalists Wednesday in Baghdad.
But, he acknowledged, there is no timeline for an assault on Fallujah or Mosul. The U.S. recently assigned advisers to Anbar province, home to Fallujah, as part of its expanding training mission.
The U.S. and its coalition allies have carried out more than 1,000 strikes in Iraq since its campaign began in August — as well as hundreds more in neighboring Syria.
American officials say the campaign has been somewhat successful, though there has been little success in stopping the flow of foreign fighters into Islamic State group territory.
Iraqi officials have grown increasingly critical of the U.S. and the coalition airstrikes. Lieutenant General Abdul-Wahab al-Saadi, who led Iraqi soldiers to recapture the oil refinery city of Beiji, said his forces lack weapons, equipment and battle-ready troops.
He also called U.S. air support erratic. Some Iraqi lawmakers say America provided greater help to the semi-autonomous Kurdish regional government in northern Iraq at the expense of the rest of the country.
Despite that, Iraqi troops and militiamen have made slow gains against the militants in an area immediately north of Baghdad in heavy fighting. They and the Kurds also have been able to push Islamic State group fighters out of parts of Diyala province on Baghdad's northeast fringe.
Further north, Iraqi and Kurdish ground forces retook the Mosul Dam in August. Kurdish forces have waged another campaign along the Syrian border toward the town of Sinjar, which they have been trying to capture for weeks.
Islamic State group fighters, meanwhile, have been advancing in western Anbar province, the heartland of Iraq's Sunni minority. The militants and Iraqi troops battle constantly for control of the provincial capital, Ramadi. Tens of thousands of civilians have fled Fallujah and Anbar provincial officials estimate that the city's population is just 15 percent of what it was a year ago.
The fall of Fallujah was a resounding humiliation for Iraq's military. Al-Sudani, the soldier stationed outside the city, recalled how militants struck troops in nightly raids last January as the city's Sunni residents protested against the military, seen as representatives of the Shiite-led government. The soldiers hunkered down as the city rapidly slipped out of government control.
"Nights were the scariest," al-Sudani said. One night, clashes broke out between troops and protesters, leaving 40 people dead. The military pulled out immediately afterward, allowing the militant takeover.
Iraq's new government, led by Prime Minister Haider al-Abadi, has worked with coalition forces to recruit Sunni tribal support as a means to battle the Islamic State group. But promises to arm and train the tribes have stalled. The Islamic State group also has massacred tribesmen, women and children across Anbar as a warning against anyone collaborating with the government.
The Islamic State group tapped into longstanding feelings of neglect and resentment by Sunnis toward the Shiite-led government in its advance. But the group risks losing some of its initial popular appeal as difficulties mount in governing the "caliphate" it declared across parts of Syria and Iraq, still home to as many as 8 million people.
Residents in Fallujah and Mosul report shortages of fruits, vegetables and cooking gas, causing significant price hikes. Power outages are frequent. The militants are growing distrustful, killing locals they believe have tipped off the U.S.-led coalition.
Abdul-Rahman Mushrif, a Fallujah grocery store owner, said two of his brothers fled the city at the height of the violence last year and have been unable to return for fear that they could be killed.
"They could not attend the funeral of our youngest brother and our father because the city is under siege," he said. "Our situation is miserable. We lack almost everything."