South Sudan's president Salva Kiir and rebel leader Riek Machar have met face-to-face for the latest round of peace talks aimed at ending their 13-month-old civil war, mediators and officials said.

Kiir and Machar, whose rival armies continue to fight it out on the ground, met on Thursday alongside mediators from the East African regional IGAD bloc in the Ethiopian capital Addis Ababa.

Kiir "is doing his duties trying to restore peace", his spokesman Ateny Wek Ateny told the AFP news agency, also dismissing reports that Kiir had fallen sick and that the talks had been cancelled.

"The meeting... was aimed at narrowing the gap in the negotiations in an attempt to arrive at finding a peaceful solution," Ateny added.

An IGAD official also confirmed the two were meeting, and were due later on Thursday to hold talks with regional leaders ahead of an African Union summit in Addis Ababa on Friday and Saturday.

The rivals last met earlier this month in Tanzania, where they signed a sixth ceasefire deal within a year, and also promised to "make a public apology to the people of South Sudan for what has happened" since war broke out in December 2013.

Since then, fighting has continued, and diplomats have been growing increasingly frustrated and impatient with the peace talks - held in luxury hotels with delegates accused of being out of touch with the suffering back home.

Failed deals

The conflict led to ethnic divisions and set off a cycle of retaliatory battles and massacres across the country that have left tens of thousands dead.

All previous agreements to end more than a year of violence collapsed within days if not hours.

Rebel military spokesman Lul Ruai Koang said in a statement on Thursday that government troops were advancing in eastern Jonglei state.

He also warned that the rebel force would create "the largest mass grave" for any troops who continued attacking.

"Any attempt … at invading our areas will meet strong resistance," Koang said.

South Sudan, the world's youngest nation, has been locked in civil war since December 2013 when Kiir accused his sacked deputy Machar of attempting a coup.