Khaled al-Mahjoub, a spokesman of Haftar’s self-styled Libyan National Army (LNA), said the fighters captured “all the districts surrounding the city”, including al-Qardabiya airbase, before moving towards the city centre.
However, Libya’s internationally recognised Government of National Accord (GNA) rejected the information in a statement, referring to it as “rumours claiming gains of militias and mercenaries of war criminal Haftar”.
GNA said the government forces repelled LNA’s attack, destroying two armed vehicles near the east of Sirte.
“The situation inside Sirte is completely under control, and the clashes that took place on the eve of this day took place outside the city,” the government said.
Earlier on Monday, LNA sources said the takeover came after forces from the city of Misrata, a key source of military power for GNA, retreated from Sirte.
A resident in Sirte city centre told Reuters News Agency by phone that they can see “convoys of LNA inside Sirte city … they control large parts of the city now. We also hear gunfire”.
Al Jazeera’s Mahmoud Abdelwahed, reporting from the capital Tripoli, said that, according to the military sources in Sirte, “Haftar’s forces took control of several parts of the city, including the port and the city centre along with the military camps in the south of the city.”
“The city is very strategic because it is very close to the oil fields and oil ports in central Libya and the coast,” he said.
“We are also getting news from the military sources in Misrata that they are sending troops to Sirte to repel the attacks of Haftar’s forces.”
Capturing Sirte would be an important gain for Haftar, who since April has been waging a military offensive on Tripoli which is home to the GNA.
Sirte lies in the centre of Libya’s Mediterranean coast, and has been controlled by GNA-aligned forces since they ejected the ISIL (ISIS) armed group from the city with the help of US air raids in late 2016.
The LNA advance comes as Turkey is deploying military advisors and experts to Libya to help shore up the GNA, part of a trend of rising international involvement in Libya’s conflict.
Haftar’s LNA has received material and military support from countries including the United Arab Emirates (UAE), Jordan and Egypt, according to UN experts and diplomats.
In recent weeks, there has been an escalation of fighting, shelling and air raids around Tripoli.
On Saturday evening, a military college in the capital was hit, killing at least 30 people, a day after the only functioning airport in Tripoli faced its latest closure due to shelling and rocket fire.
Sirte, the birthplace of former Libyan leader Muammar Gaddafi, was taken over by ISIL in early 2015, becoming the group’s most important base outside the Middle East.
The city is just to the west of Libya’s oil crescent, a strip of coastline along which several key oil export terminals are located. Haftar’s forces seized the oil ports in 2016.