The UN High Commissioner for Human Rights pointed out that her office was continuing to receive information of ongoing fighting in central Tigray in particular.
US Secretary of State Antony Blinken, in a telephone call with Abiy on Monday, urged Ethiopia to allow an independent, international probe into allegations of mass killings.
Blinken noted Ethiopian commitments to full accountability, including international support for investigations into human rights abuses and to allowing unhindered humanitarian access.
"They are receiving support from the South Sudanese Ministry of Refugee Affairs," Dujarric continued, and the UN High Commissioner for Refugees (UNHCR) is "aware" of the situation and in contact with South Sudanese authorities.
Abiy declared victory in late November when federal forces took the Tigray capital Mekele, but Debretsion, president of Tigray when the fighting started, has remained on the run.