ISIS took over Sirte last year, exploiting Libya's turmoil to gain a foothold in the oil-rich country.
Brigadier General Mohammed al-Ghasri said his forces remain steadfast and aim to take control of the city before the end of the holy month of Ramadan, which began on 6 June.
Sirte was the only ISIS-held city outside Iraq and Syria, where the group controls vast swaths of territory and several cities and towns.
For weeks, government forces have fought to dislodge Daesh, pounding the port city from the air and land as ground troops wage street battles.
Forces loyal to Libya's internationally backed government say they have recaptured both the port and airport of Sirte from Daesh, forcing the armed group to retreat.
The Libyan forces also retook residential areas in the east of Sirte, which for the past year has been the main Daesh base in the North African country, a spokesman for the forces, Rida Issa, told the AFP news agency on Saturday.
“Daesh fighters are now surrounded in a densely populated area of around five square kilometres inside the city, where they are laying booby traps,” he said.
The fall of Sirte, the hometown of ousted leader Muammar Gaddafi, would be a major setback for Daesh, who have also lost territory in Syria and Iraq, where they have declared a "caliphate".
"We will liberate the city of Sirte from Daesh and its terrorism. We will clean up all of Libya and defeat anyone who opposes us in our country," unity government fighter Omar Rhaal said.
Foreign intelligence services estimate Daesh has 5,000 fighters in Libya, but its strength inside Sirte, which Daesh has held since June 2015, is unclear.
A total of 137 UN-backed government forces have been killed and 500 wounded since the beginning of the operation on May 12, according to a medical official in the western city of Misrata.
Daesh militants targeted Libyan forces on Sunday with a series of car bombs in the port city of Sirte, killing at least one paramedic.
Brigadier General Mohammed al-Ghasri said Sunday that the terrorists attacked forces loyal to Libya’s unity government with bombs hidden in an ambulance and two other vehicles earlier in the day.
Two of the bomb attacks reportedly hit gatherings of pro-government troops and the third one hit a field hospital.
Ghasri said the attackers “infiltrated our siege” on the main stronghold of Daesh in the North African country and targeted medical units and supply lines.
"Sirte, the major Daesh stronghold outside Iraq and Syria, had fallen into the hands of the group in February 2015. The full recapture of the city is a major boost to the Government of National Accord (GNA), which has come to office through support from the United Nations."
One paramedic was killed and a number of soldiers were wounded, he said, adding, "They aimed to shake our ranks, to force us to retreat, but we remain steadfast. We are determined to finish the job before the end of the holy month of Ramadan."
He further noted that Daesh militants have moved into a populated area in the center of Sirte and their snipers have been taking positions on rooftops to shoot Libyan troops.
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