Prime Minister Haider al-Abadi said on Tuesday that the country's relations with Turkey were no longer strained and were back on track, also announcing that about three months were needed to remove Daesh from Iraq.

Abadi announced the new plan after responding to comments by the commander of the U.S.-led coalition supporting Iraqi forces that it would take as long as two years to eliminate Daesh and its cells in Iraq and neighbouring Syria.

"The Americans were very pessimistic. They used to talk about a really long period, but the remarkable successes achieved by our brave and heroic fighters reduced that. I foresee that in Iraq it will take three months," he said.

The announcement comes as U.S.-backed forces battle to dislodge the militants from Mosul, their last major stronghold in the country.

Abadi had previously pledged the northern city would be retaken by the end of this year. But the operation has been slowed by concern to avoid casualties among civilians, who have mostly stayed in their homes rather than fleeing as was initially expected.

Overnight the coalition bombed the last remaining bridge connecting the eastern and western parts of Mosul "to reduce enemy freedom of movement", a spokesman said on Tuesday.

More than two months into the Mosul operation, elite Iraqi soldiers have retaken a quarter of the city, but entered a planned "operational refit" this month.

Earlier this year, Iraqi-Turkish relations had turned sour over who should take part in the planned Mosul assault against Daesh.

Iraq had said they perceived the Turkish military forces presence in the country as a violation of Iraqi sovereignty and had called upon the Turkish authorities to withdraw those forces as soon as possible.

However, Turkey had stated that Turkish forces had initially been stationed at the Bashiqa camp to train the local forces in their fight against Daesh at the request of Abadi, himself.

About 150 soldiers and up to 25 tanks were stationed in Bashiqa to protect Turkish servicemen training Iraqi volunteers to fight Daesh since March 2015. Turkey had pointed out that the soldiers were not assigned to combat duties, and would do all it could to prevent the operation from deepening sectarian conflict on its borders.

Mosul, the largest city seized by Daesh anywhere across the once vast territory it controlled in Iraq and neighbouring Syria, has been held by the group since its fighters drove the U.S.-trained army out in June 2014.

Besides Mosul, Daesh still controls the towns of Tel Afar and Qaim as well as Hawija and the surrounding area.

The city's fall would probably end Daesh's ambition to create a so-called caliphate, but the fighters could still mount a more traditional insurgency in Iraq, and plot or inspire attacks on the West.