
What's the latest from the Tigrayan capital?
Details of the fighting are hard to confirm because all phone, mobile and internet communications with the Tigray region have been cut.
However, in a statement on Twitter, Mr Abiy said the army was in full control and that this "marks the completion of the [military's] last phase".
"I am pleased to share that we have completed and ceased the military operations in the Tigray region," he said.
The army had released thousands of soldiers taken by the TPLF and was in control of the airport and regional offices, Mr Abiy said, adding that the operation had been carried out with "due care for citizens".
There have been fears for the 500,000 people living in the city.
Mr Abiy said: "We now have ahead of us the critical task of rebuilding what has been destroyed... [and] returning those who have fled."
Earlier, TPLF leader Debretsion Gebremichael told Reuters in a text message that Mekelle was under "heavy bombardment".
A separate TPLF statement, reported by AFP, urged "the international community to condemn the artillery and warplane attacks and massacres being committed".

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