TIKRIT, Iraq (Reuters) - Islamic State has captured most of a village south of Mosul despite losing control of its stronghold in the city, an Iraqi army officer and residents said, deploying guerrilla-style tactics as its self-proclaimed caliphate crumbles.

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Prime Minister Haider al-Abadi declared victory over Islamic State in Mosul on Monday, marking the biggest defeat for the hardline Sunni group since its lightning sweep through northern Iraq three years ago.

But the militants, armed with machine guns and mortars, have now seized more than 75 percent of Imam Gharbi, a village on the western bank of the Tigris river some 70 km (44 miles) south of Mosul, and reinforcements are expected, the Iraqi army officer said.

Islamic State launched its attack on Imam Gharbi last week, in the kind of strike it is expected to deploy now as U.S.-backed Iraqi forces regain control over cities the group captured during its shock 2014 offensive.

Mosul resident Hind Mahmoud said by telephone that she had heard exchanges of gunfire in the Old City and seen an Iraqi army helicopter firing on Islamic State militants on Tuesday.

The top U.S. general in Iraq said that security forces would still need to clear Islamic State hideouts in Mosul, where as many as a couple of hundred fighters could remain, and would rest before fighting against the group in Tal Afar.

Lieutenant General Stephen Townsend told a news briefing in Washington that some Islamic State militants in Mosul had offered to surrender.

In one instance yesterday, Townsend said, an Islamic State commander had told Iraqi forces that a group of fighters were willing to surrender. However, the militants wanted to surrender as a large group, which was rejected by Iraqi forces who believed it could be a trap.

“We saw then later in the day, a wave of suicide attacks come out and we assess that was actually a ploy, a desperate ploy by an ISIS leader to actually get the Iraqi security force to allow a large group of fighters to come out and allow them to get close before they sprung an attack,” Townsend said.

Some militants had offered to surrender today as well, but Townsend did not know the results of those negotiations.

Stripped of Mosul, Islamic State’s dominion in Iraq will be reduced to mainly rural, desert areas west and south of the city.

Islamic State also faces pressure in its operational base in the Syrian city of Raqqa, where U.S.-backed Syrian Kurdish and Arab forces have seized territory on three sides of the city.

The campaign to retake Mosul from the militants was launched last October by a 100,000-strong alliance of Iraqi government units, Kurdish Peshmerga fighters and Shi’ite militias, with a U.S.-led coalition providing key air and ground support.

Abadi’s government in Iraq now faces a difficult task managing the sectarian tensions which enabled Islamic State to gain supporters in the country among fellow Sunnis, who say they were marginalized by the Shi’ite-led government.

The U.S.-led coalition warned that victory in Mosul did not mark the end of the group’s global threat.

“Now it is time for all Iraqis to unite to ensure ISIS (Islamic State) is defeated across the rest of Iraq and that the conditions that led to the rise of ISIS in Iraq are not allowed to return again,” Townsend said in a statement on Monday.