More than eight months since the operation to retake Mosul was launched, IS has gone from fully controlling the city to holding a few neighbourhoods on its western side.
"The number is... more or less 300 fighters, most of them of European nationalities, Arabs of other nationalities or of Asian origin," said Staff Brigadier General Nabil al-Fatlawi, a commander in the elite Counter-Terrorism Service (CTS).
"We are not able to specify when the battles will end because of the narrow type of streets in the Old City and also the presence of civilian detainees," Fatlawi said, referring to residents being used as human shields by IS.
"But I can say within days," he said.
Earlier in the day, Iraq's Joint Operations Command announced CTS forces had recaptured the Makawi area of the Old City, in a further blow at the heart of the jihadists' cross-border "caliphate".
Iraqi forces have been closing in on the Old City for months, but its narrow streets and closely spaced buildings combined with a large civilian population made for an extremely difficult fight.
Security forces recaptured a series of nearby districts, cornering the jihadists, and launched an assault inside the Old City on June 18.
They have since made significant progress.
On Saturday, officers announced the recapture of a hospital and its surroundings north of the Old City, removing a nearby but unconnected pocket of IS resistance.
Interior ministry forces recaptured the Ibn Sina hospital along with other medical facilities including a blood bank and a clinic, said Staff Lieutenant General Abdulamir Yarallah.
IS has occupied several of Mosul's hospitals during the battle for the city.
Some security personnel have complained that restrictions on using heavy weapons against hospitals, intended to protect the facilities, have made operations riskier and more time-consuming.
Suicide bombing kills 14
Federal police chief Lieutenant General Raed Shakir Jawdat said the area around the hospital, Al-Shifaa, had been completely retaken, limiting IS's presence in Mosul to the Old City.
"Our forces are advancing from three sides and are pursuing the terrorist groups in the few remaining areas of the Old City," said Jawdat.
On Thursday, Iraqi forces retook the remains of the Grand Mosque of al-Nuri in their greatest symbolic victory since the battle began.
IS chief Abu Bakr al-Baghdadi gave a triumphal sermon at the mosque after the jihadists captured Mosul in 2014, calling on Muslims to obey him.
The mosque thus became a symbol of Baghdadi's rule and IS's "caliphate".
The jihadists made sure that the Nuri mosque was not captured intact, blowing it up as Iraqi forces closed in, along with its famed leaning minaret -- known affectionately as "Al-Hadba" (The Hunchback).
Even though it lies in ruins, the mosque's recapture has provided a boost to Iraq's forces and its government. Prime Minister Haider al-Abadi declared the jihadists' "caliphate" was coming to an end.
The next day, a senior Iraqi commander said victory in Mosul would be declared within the "next few days".
IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led coalition air strikes have since regained much of the territory they lost.
The recapture of Mosul will not however mark the end of the war against IS.
The jihadist group holds territory elsewhere in Iraq as well as in neighbouring Syria, and has been able to carry out attacks in government-held areas.
The jihadist group has also inspired "lone wolf" attacks overseas.
Highlighting the major security challenges Iraq will face after Mosul, a suicide bomber attacked a camp for displaced people west of Baghdad on Sunday, killing 14 people and wounding 13, a police major and a doctor said.
There was no immediate claim of responsibility for the attack in Anbar province, but IS frequently carries out suicide bombings against civilians in Iraq.
The camp is located west of Ramadi, a city that was recaptured from IS along with Fallujah and other parts of Anbar province, but IS still controls areas closer to the Syrian border and carries out attacks in government-held territory.
