U.S. Secretary of State Mike Pompeo on Monday urged a stop to all fighting in Ethiopia, as Prime Minister Abiy Ahmed lauded his troops for what he termed their victory in the Tigrayan capital of Mekelle.  

"I spoke with Ethiopian Prime Minister @AbiyAhmedAli today and urged a complete end to the fighting in Tigray, a start to dialogue, and free, safe, unhindered humanitarian access," Pompeo wrote on Twitter.

Claims of violence and death tolls have been impossible to confirm, as telecommunications and internet service have been cut in Tigray since fighting began. Abiy announced a military offensive against the regional government in Tigray on November 4, saying it was in response to an attack by Tigray forces on a federal military base. 

Leaders of the Tigray People's Liberation Front (TPLF) told the Reuters news agency that fighting continues.

Late Sunday, Reuters reported that TPLF leader Debretsion Gebremichael claimed in a text message to the news agency that Tigrayan forces had shot down an Ethiopian plane and taken a town from federal forces.

There was no immediate comment to such claims from the government or the military. Government sources said TPLF leaders remained on the run.

Authorities have not confirmed whether there were any deaths in a Saturday offensive, which followed a 72-hour ultimatum for the TPLF to surrender to the national government. But the International Committee of the Red Cross noted that the Ayder Referral Hospital in Mekelle was lacking body bags for the deceased.     

Meanwhile, local hospitals in Mekelle were running out of medical supplies to treat the injured, aid workers said Sunday.

According to the ICRC, roughly 80% of patients at the hospital were suffering from trauma injuries. 

"The hospital is running dangerously low on sutures, antibiotics, anticoagulants, painkillers and even gloves," Maria Soledad, head of operations for the ICRC in Ethiopia, was quoted as saying in a Sunday press release from the ICRC.

"The influx of injured comes more than three weeks after supply chains were disrupted into Mekelle," she added. 

Tens of thousands have fled the area for neighboring Sudan. Some reports say thousands have been killed since the violence broke out. 

Meanwhile, the U.N. refugee agency has appealed for $147 million to support the Ethiopians who have fled to Sudan. The agency says some 43,000 people have gone to the neighboring country in recent weeks.