By Emma Farge

GENEVA (Reuters) - A major humanitarian crisis is unfolding in Ethiopia, the United Nations refugee agency said on Tuesday, with more than 27,000 people now having fled heavy fighting to Sudan.

“People are coming out of Ethiopia really scared, afraid, with stories saying they have been fleeing heavy fighting and there’s no sign of the fighting stopping,” Babar Baloch, spokesman of the U.N. High Commissioner for Refugees (UNHCR), told a Geneva news briefing.

Ethiopia’s prime minister warned on Tuesday that a deadline for rebel northern forces to lay down arms had expired, paving the way for a push on the Tigray region’s capital in the two-week conflict destabilising the Horn of Africa.

“UNHCR is warning that a full-scale humanitarian crisis is unfolding as thousands of refugees flee ongoing fighting in Ethiopia’s Tigray region each day to seek safety in eastern Sudan,” Baloch said.

“UNHCR is on stand-by to provide assistance in Tigray when access and security allow,” he added.

Jens Laerke, spokesman of the U.N. Office for the Coordination of Humanitarian Affairs (OCHA), told the briefing: “There may be massive displacement inside Tigray and that is of course a concern and we try to prepare the best way possible.”

Baloch also repeated concerns for tens of thousands of Eritrean refugees settled in Ethiopia, saying that clashes had occurred near to one of the settlements, but that poor communications were complicating aid efforts.

Humanitarian access was a priority, added OCHA’s Laerke, saying negotiations were ongoing. “We are in continuous contact with the federal government and relevant regional authorities,” he told the briefing.

(This story has been corrected to change wording from U.N. official in paragraph 10 to show that “humanitarian access” is a priority, not “the creation of a humanitarian corridor”)