REUTERS/Goran Tomasevic
A fighter of Libyan forces allied with the U.N.-backed government runs for cover during a battle with Islamic State fighters in Sirte, Libya, July 31, 2016.
"Our forces have complete control of the whole of the Ouagadougou (convention) complex - they even advanced some distance beyond the complex," said Rida Issa, a spokesman in the forces' media office.
Issa also said it was not clear how the plane crashed. Islamic State said it had shot down the jet, killing the pilot, according to a statement on a website close to the jihadist group.
Forces aligned with Libya's U.N.-backed government launched their campaign for Sirte in May. On Aug. 1, the United States began air strikes to help them advance against militants encircled in the center of the Mediterranean coastal city.
And US Special Operations troops have been spotted on the ground in Sirte. Although the special operators have not directly engaged in combat, they are playing a support role assisting Libyan forces and guiding airstrikes against ISIS in the city.
U.S. drones and fighter jets have carried out a total of 29 strikes since then, targeting several IS emplacements on Monday and a gun-mounted pick-up truck on Tuesday, according to statements by U.S. Africa Command.
Libyan fighter jets have also been flying regular missions over Sirte, the hometown of late dictator Muammar Gaddafi, whose fall in an 2011 uprising precipitated years of factional anarchy in the oil-exporting North African country.
The U.N.-backed government arrived in Tripoli in March, but has struggled to impose its authority and faces continuing resistance from armed factions that control eastern Libya.
On the ground in Sirte, Libyan forces led by brigades from the city of Misrata have suffered heavy casualties from Islamic State mines and sniper fire. Clashes have been sporadic, with heavier fighting interspersed with lulls that last for several days.
Goran Tomasevic/Reuters
A fighter of Libyan forces allied with the U.N.-backed government fires a shell with Soviet made T-55 tank at Islamic State fighters in Sirte, Libya, August 2, 2016.
"Our forces are making progress in their attack against Daesh (Islamic State), and have recaptured the University of Sirte," Issa said. They had also advanced to a cluster of unfinished buildings used by Islamic State snipers just west of the center of Sirte, he said.
The latest clashes came after the government-backed fighters reached a hotel complex southeast of the recently captured Dollar neighborhood on Monday.
Libyan militants returning from combat in Syria's civil war helped implant Islamic State in Libya in 2014, but IS has struggled to win support or hold territory as most local people regard it as a malign import dependent on foreign fighters.
(Reuters reporting by Ahmed Elumami; writing by Aidan Lewis; editing by Mark Heinrich)