Ethiopian Prime Minister Abiy Ahmed said Monday the Tigray region's dissident leaders had fled west of the regional capital after weeks of fighting but indicated federal forces were monitoring them closely and would attack them soon.

Abiy, winner of last year's Nobel Peace Prize, this month ordered military operations against leaders of Tigray's ruling party, the Tigray People's Liberation Front (TPLF), in response to what he said were TPLF-organised attacks on Ethiopian federal army camps.

More than three weeks of fighting between federal soldiers and pro-TPLF forces has left thousands dead in the northern region, and prompted tens of thousands of refugees to flee across the border into Sudan.

"I want them to hear me: yesterday evening, around midnight, we saw them from the situation room in the area between Hagere Selam and Abiy Addi," Abiy said in remarks to lawmakers, referring to two towns west of the Tigray capital Mekele.

"We didn't attack them at night because as they retreated they took their wives, children and abducted soldiers... But this will not continue."

The fighting has been a dramatic escalation of tensions between Abiy and the leaders of the TPLF, which dominated Ethiopian politics for nearly three decades before anti-government protests swept Abiy to office in 2018.

Abiy said on Saturday the military operations were "completed" after federal forces claimed control of the Tigray regional capital Mekele.

The TPLF leaders, however, have repeatedly vowed to fight on as long as federal forces are on Tigrayan soil.

Their exact whereabouts remain unknown.

'Mekele is ours'

As the Ethiopian military bore down on Mekele last week, global concern mounted about a possible bloodbath in a city that, before the conflict, had a population of half a million.

A communications blackout in Tigray has made it difficult to verify claims from both sides about how the fighting is going.

On Monday, Abiy claimed soldiers did not kill any civilians as they took over Mekele and other cities in Tigray.

"Mekele is ours, it was built with our own resources. We are not going to destroy it," he said. "Not even a single person was harmed by the operation in Mekele."

The International Committee of the Red Cross said Sunday that hospitals in Mekele were flooded with trauma patients, though it did not specify how the injuries were sustained.

Abiy also dismissed claims from TPLF leader Debretsion Gebremichael that airstrikes had resulted in many civilian casualties.

As Abiy tries to shift towards helping Tigray recover, the national human rights body called Monday for telecommunications to be restored and for water, electricity, and health services to resume.

The Ethiopian Human Rights Commission (EHRC), which is government-affiliated but independent, also noted "complaints of ethnic profiling" including "forced leave from work" and travel restrictions.

"EHRC is gravely concerned that while there is no government policy nor legal framework condoning ethnic profiling, security measures designed t