The first names for a new Libyan unity government could emerge this week after progress in UN-mediated talks between its warring parties, UN special envoy Bernardino Leon said Monday.

The first names for a new Libyan unity government could emerge this week after progress in UN-mediated talks between its warring parties, UN special envoy Bernardino Leon said Monday.

Leon was in Brussels for a conference of Libyan mayors after visiting Morocco, where he has been working with representatives of Libya's rival parliaments to reach a deal to end months of fighting.

"There is a chance that we can make progress and have the first names for a unity government this week," Leon told reporters.

"It is going to be a difficult discussion and I wouldn't like expectations to be too high, bearing in mind how difficult the situation is on the ground. But there is a possibility and we will do our best to reach there by the end of this week."

Leon had said on Sunday that the first documents to pave the way for a unity government could be ready within two days.

Libya has been in turmoil since the overthrow of Moammar Gaddafi in 2011 by rebels backed by US, French and British air strikes.

Libya has had two governments and parliaments since the capital Tripoli was seized in August 2014 by Fajr Libya, a militia alliance which includes Takfiris that has installed its own government and legislature.

On Friday the internationally recognized cabinet based in the eastern city of Tobruk said loyalist forces had launched an offensive to "liberate" Tripoli.

The Tripoli parliament's delegation threatened to walk out of the current peace talks in the Moroccan resort of Skhirat when the fighting erupted at the end of last week.