Rebellious forces from Ethiopia's northern region of Tigray said they had shot down a military plane and retaken a town from federal forces on Sunday, a day after the prime minister announced federal troops had taken over the regional capital and military operations were complete.

There was no immediate comment from the government or the military on the claims made by Debretsion Gebremichael, leader of the Tigray People's Liberation Front (TPLF) in text messages to Reuters.

Claims from all sides are difficult to verify since phone and internet links to Tigray have been down and access tightly controlled since the fighting began on Nov. 4.

Prime Minister Abiy Ahmed's government has been trying to quell a rebellion by the TPLF, a powerful ethnically-based party that dominated the central government from 1991 until Abiy came to power in 2018.

Thousands of people are believed to have been killed and nearly 44,000 have fled to Sudan since the fighting began. The conflict has been another test for Abiy, who took office two years ago and is trying to hold together a patchwork of ethnic groups that make up Ethiopia's 115 million people.

Abiy said on Saturday evening federal troops had taken control of the Tigrayan capital Mekelle within hours of launching an offensive there, laying to rest fears of protracted fighting in the city of 500,000 people.

The prime minister, who refers to the three-week-old conflict as an internal law and order matter and has rebuffed international offers of mediation, said federal police would now try to arrest TPLF "criminals" and bring them to court.

It was not clear if any TPLF leaders had surrendered or been apprehended since Saturday. Their whereabouts are also unknown.

TPLF leader Debretsion said on Saturday evening in a series of text messages to Reuters that his forces were withdrawing from around the city but would fight on, raising the spectre of a drawn-out guerrilla war.

In text messages on Sunday, he said that his forces had shot down an Ethiopian military plane and captured the pilot, and had also retaken the town of Axum.

Also on Sunday, Ethiopian state TV (ETV) said on Sunday that 70 graves, some individual and some containing multiple bodies were found in the town of Humera in Tigray. The news reader did not say who might have killed the people buried in the graves.

Regional diplomats and experts have warned that a rapid military victory might not signal the end of the conflict.

The TPLF has a history of guerrilla resistance. Tigray's mountainous terrain and borders with Sudan and Eritrea helped the TPLF during its long struggle against Marxist dictator Mengistu Haile Mariam, whom it eventually toppled in 1991.