Ethiopian forces have reportedly taken back towns near Addis Ababa, including Shewa Robit, which were captures by the rebels last week.
Ethiopia has claimed it has recaptured several towns after Tigrayan rebels took control of them last week as part of their advance towards the capital.
Government spokesman Legesse Tulu said on Wednesday that Ethiopian forces took back towns nearby capital Addis Ababa, including Shewa Robit which is around 220 kilometres away.
"In Shewa front, the Mezezo, Molale, Shewa Robit, Rasa and its surroundings have been freed from the terrorist TPLF," Legesse said in comments broadcast on state media.
Legesse was referring to the Tigray People's Liberation Front group which has been locked in a war with Abiy's government since November 2020.
He also said the government would "in a short period of time" retake Dessie and Lalibela, a UNESCO World Heritage site that fell to the rebels in August.
Meanwhile, fighting has reportedly spread to Debre Sina, a town located less than 200 kilometres by road from Addis Ababa.
March on Addis Ababa
The conflict took a sharp turn around a month ago, when the TPLF claimed to have captured the strategic towns of Dessie and Kombolcha, located on a key highway to the capital.
Abiy last week announced he would head to the battlefield as fighting reportedly rages on at least three fronts in the country.
In recent days, state media has broadcast images of a uniformed Abiy, a former lieutenant colonel in the military, in what appeared to be the northeastern region of Afar.
On Sunday, state media claimed the army controlled the lowland Afar town of Chifra, and Abiy said on Tuesday such gains would be replicated in Amhara region, where Dessie lies.
Fears of a rebel march on Addis Ababa have prompted the United States, France, Britain and other countries to urge their citizens to leave Ethiopia as soon as possible.
Abiy's government says TPLF gains are overstated and the city is secure.
The fighting has killed thousands, displaced more than two million and driven hundreds of thousands into famine-like conditions, according to UN estimates.