Forces loyal to Libya's internationally backed government say they are close to retaking Sirte from the Islamic State of Iraq and the Levant (ISIL) group after capturing a key neighbourhood in the heart of the coastal city.

The fighters, mainly from the nearby city of Misrata, said they were advancing on ISIL-held "District One", after seizing "District Two" on Tuesday.

"District Two has been liberated," Reda Issa, a spokesman for the pro-government forces, told the Reuters news agency.

"The neighbourhood is now completely under control of our forces," he said, adding that his side had overcome fierce opposition from ISIL snipers and car bombs.

The advance came a day after loyalists cleared and demined areas captured in earlier clashes.

ISIL, also known as ISIS, seized control of Sirte, the birth place of Libya's overthrown leader Muammar Gaddafi, last year and controlled about 250km of the country's Mediterranean coastline before forces aligned to the nascent, UN-brokered Government of National Accord (GNA) began operations against it in May.

READ MORE: How serious is the ISIL threat in Libya?

Since August 1, their progress has been aided by US air strikes on ISIL vehicles, weapons and fighting positions.

US President Barack Obama said it was "in America's national security interest" to help the pro-government forces "finish the job" of ousting ISIL from Sirte.

The internationally backed government's forces and those of a rival authority in the east are currently engaged in a race to be the first to drive ISIL out of the city.

But some analysts believe this could jeopardise efforts to defeat the armed group.

Libya has suffered from chaos since the 2011 overthrow of Gaddafi, with numerous revolutionary militias formed along regional and ideological lines vying for power.