The fight is about self-determination of the region of about six million people, the Tigray leader said, and it "will continue until the invaders are out".
After securing control of western Tigray and giving TPLF leaders a 72-hour ultimatum to surrender, Abiy announced Thursday he had ordered a "final offensive" on Mekele.
Federal forces captured regional capital Mekelle at the weekend and declared victory over the Tigray People's Liberation Front (TPLF), a guerrilla movement-turned-political party that dominated the federal government for almost three decades until 2018.
A woman braids a girl's hair in the Hamdeyat refugee transit camp, which houses Ethiopian refugees fleeing the fighting in the Tigray region, on the Sudan-Ethiopia border, Sudan, November 30, 2020.
Ethiopian Prime Minister Abiy Ahmed said Monday Tigray region's dissident leaders had fled west of the regional capital after weeks of fighting, but said federal forces were monitoring them closely and would "attack" them soon.
Debretsion said that fighting persisted Tuesday in at least three locations, two of which were "around Mekele" and another near the town of Wukro, 50 kilometres (31 miles) north. The TPLF denied it carried out such an attack.
As for the idea of talks with the government, something Abiy has repeatedly rejected, the Tigray leader said that "depends on the content", and Ethiopian forces would first have to leave the region.
It remained impossible to independently verify whether the regional capital Mekele was completely under federal government control, though a military spokesman told AFP operations were proceeding "very well".
"Civilian casualties are so high", he said, though he denied having any estimate of the toll.
The TPLF has considerable military assets, and at the outset of the conflict analysts estimated it could mobilise 200,000 troops.
Debretsion said it still boasted many "experienced fighters" as well as "heavy artillery".
There were no new engagements Monday but "probably tomorrow we will have fighting", he added.
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.
Claims from all sides are hard to verify since phone and internet links to Tigray have largely been down and access has been tightly controlled since the war began.
However, in an address to parliament on Monday, Prime Minister Abiy Ahmed claimed in parliament soldiers did not kill any civilians as they took over Mekele and other cities in Tigray. It was built by our resources, we are not going to destroy it.
"There are skirmishes continuing in many parts of Tigray and we are seeing the hallmarks of the beginning of an insurgency", Horn of Africa expert Rashid Abdi told an online forum.
Abiy said "not even a single person" was injured by the operation in Mekelle, AFP reported.
Hospitals and health centres in the Tigray region are running "dangerously low" on supplies to care for the wounded, the International Committee of the Red Cross has said.
Ethiopia is a major contributor to an African Union peacekeeping force fighting Al Qaeda-linked militants in Somalia, but has disarmed several hundred soldiers of Tigrayan ethnicity, questioning their loyalty.
He urged the Government to respect the human rights of Tigrayans and all ethnic groups.
During an address to Ethiopian parliamentarians lasting nearly four hours, Abiy heaped praise on Ethiopian troops, describing them as "disciplined" and "victorious".
The party has complained of being sidelined, targeted for corruption prosecutions and scapegoated for the country's woes under Abiy's rule.
It then tried to brand Abiy an illegitimate ruler.
He accused the TPLF of fomenting internal conflict, including ethnic clashes, throughout the country during his tenure, leaving only Tigray unaffected.