GENEVA (Reuters) - Nearly 100,000 Eritrean refugees in Ethiopia's Tigray region will run out of food as early as next week if parties to the conflict do not allow humanitarian access, the U.N. refugee agency said on Friday.

African peace envoys met with Ethiopian Prime Minister Abiy Ahmed on Friday, a day after he said that the military was beginning the "final phase" of an offensive which rights groups fear could bring huge civilian casualties.

The UNHCR says 96,000 Eritrean refugees are living in four camps in Tigray, with some reported to have been in the vicinity of recent clashes.

"They would be running out of food as of Monday - we are ready with our supplies trying to reach these populations," UNHCR spokesman Babar Baloch told a Geneva briefing, saying the estimate was based on calculations since the last distribution some weeks ago.

"What is needed is unhindered humanitarian access to reach them as soon as possible," he added.

He declined to specify who was blocking access but said that the call for access applied to both the Ethiopian military and the Tigray People's Liberation Front.

The United Nations, which still has staff in Tigray, has been negotiating with all parties to the conflict for access but there is no sign yet of a breakthrough.

Communication with remaining staff has been poor due to a telecommunications blackout, Baloch added. The conflict has forced some 43,000 people to flee across the border to Sudan.

Many of the Eritrean refugees in Ethiopia arrived more than a decade ago amid ongoing tensions between the two countries despite the end of a two-year border war between the neighbors.

A final peace deal was only agreed in 2018 by Abiy, who won the Nobel peace prize for his achievement.