MOSUL, Iraq -- Iraq's Prime Minister declared an end to the Islamic State of Iraq and Syria (ISIS) caliphate Thursday after Iraqi forces captured captured the compound of a landmark mosque in Mosul that was blown up last week by ISIS militants -- a hugely symbolic site from where the top ISIS leader declared an Islamic caliphate nearly three years ago.

"We are seeing the end of the fake Daesh state. The liberation of Mosul proves that," Haider al-Abadi said using the Arabic acronym for ISIS in a statement posted to Twitter. "We will not relent, our brave forces will bring victory."

But even as the Iraqi leader issued his statement, heavy clashes continued to unfold in Mosul -- filling field hospitals and forcing hundreds to flee.

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Iraqi troops are pushing deeper into the Old City, a densely populated neighborhood west of the Tigris River where the al-Nouri Mosque, with its 12th century al-Hadba minaret, once stood and where the ISIS militants are now making their last stand in what are expected to be the final days of the battle for Mosul, Iraq's second-largest city.

According to U.S. military spokesman Col. Ryan Dillon, a couple hundred ISIS fighters remain in two locations -- some inside the Old City and the rest at a hospital complex to the north, CBS News correspondent David Martin reports.

The complete liberation of Mosul is "closer to days versus weeks" away, Dillon says.

Iraqi special forces reached the al-Nuri Mosque compound and took control of the surrounding streets on Thursday afternoon, following a dawn push into the area, Lt. Gen. Abdul Wahab al-Saadi of the elite force told The Associated Press.

Damaged and destroyed houses dot the route Iraqi forces have carved into the congested district -- along a landscape of destruction where the stench of rotting bodies rises from under the rubble.

Thursday's push comes more than a week after Iraqi forces launched the operation to retake Mosul's last ISIS-held parts of the Old City neighborhood, with its narrow alleyways and dense clusters of homes.

Taking the mosque is a symbolic victory -- from its pulpit, ISIS leader Abu Bakr al-Baghdadi declared a self-styled Islamic "caliphate" on July 4, 2014, encompassing territories then-held by ISIS in Syria and Iraq.

In a report issued Thursday, conflict monitoring group IHS Markit said ISIS' territories in those two nations had shrunk 60 percent and its revenues by 80 percent in the space of about two years, "meaning the group is unlikely to survive its fourth year" -- at least in its current form.

Iraqi and coalition officials said ISIS blew up the mosque complex last week. ISIS blamed a U.S. airstrike for the destruction.

After months of fighting, the terror group's hold on Mosul has shrunk to less than a square mile of territory, but the advances have come at considerable cost.

"There are hundreds of bodies under the rubble," said special forces Maj. Dhia Thamir, deployed inside the Old City. He added that all the dead bodies along the special forces' route were of ISIS fighters.

As CBS News correspondent Charlie D'Agata reported this week, the Iraqi military has opened exit routes for shell-shocked residents to flee the Old City, with the U.N. warning of a rising civilian death toll and the "unimaginable" risks facing those trapped inside.

As the battle enters its final phase, Iraqi soldiers are locked in a fight against ISIS holdouts -- and against time to try and save the thousands of civilians still trapped.

Special forces Maj. Gen. Sami al-Aridi acknowledged that some civilians had been killed by airstrikes and artillery in the fight for the Old City. "Of course there is collateral damage, it is always this way in war," he said.

"The houses are very old," he said, referring to the Old City, "so any bombardment causes them to collapse completely."

Al-Aridi said the clearing of the mosque would likely require specialized engineering teams since the militants likely rigged the site with explosives.