The United Nations (UN) human rights chief said on Friday he was "horrified" by escalating violence near Sudan's al-Fashir and held discussions this week with commanders from both sides of the conflict, warning of a humanitarian disaster if the city is attacked.

Hundreds of thousands of people are sheltering in al-Fashir without basic supplies amid fears that nearby fighting will turn into an all-out battle for the city, the Sudanese army's last stronghold in the western Darfur region.

Its capture would be a major boost for the rival Rapid Support Forces (RSF) as regional and international powers try to push the sides to negotiate an end to a 13-month war.

Ravina Shamdasani, spokesperson for High Commissioner Volker Turk, said Turk had held two parallel phone calls this week with Sudan army chief General Abdel Fattah al-Burhan and the leader of the RSF, Mohamed Hamdan Dagalo, urging them to de-escalate.

"The High Commissioner warned both commanders that fighting in (al-Fashir), where more than 1.8-million residents and internally displaced people are currently encircled and at imminent risk of famine, would have a catastrophic impact on civilians, and would deepen intercommunal conflict with disastrous humanitarian consequences," she said at a UN press briefing in Geneva, adding that Turk was "horrified" by recent violence there.

The UN human rights office said at least 58 people had been killed around al-Fashir since last week.