The Ethiopian government said its army was clearing rebellious Tigrayan forces from the northern Amhara and Afar regions, dismissing Tigrayan statements that forces were retreating voluntarily to create an "opening for peace".
Thousands of civilians have been killed as a result of the13-month-old conflict while about 400,000 are facing famine conditions in Tigray and 9.4 million people need food aid across northern Ethiopia.
The TPLF, the party that controls the Tigray region in the far north of Ethiopia and is at war with the government, had announced its withdrawal from neighbouring Amhara and Afar yesterday.
"As we have seen in recent weeks, the national defence forces together with allied forces from the Afar region and the Amhara region have made considerable gains in reversing the occupation by TPLF of many Amhara and Afar towns," government spokeswoman Billene Seyoum told a news conference.
"These gains have been made in very heavy battles that have been undertaken over the past weeks, the most recent being the full clearing of TPLF from North Wollo Zone and liberating its strategic capital Woldiya," Ms Billene said.
She said the national armed forces were still in the process of clearing TPLF forces from pockets within the two regions.
TPLF leader Debretsion Gebremichael has written to the United Nations calling for a no-fly zone for hostile aircraft over Tigray, arms embargoes on Ethiopia and its ally Eritrea, and a UN mechanism to verify that external armed forces have left Tigray.
Asked about the letter, Ms Billene did not comment in detail on its contents.
"I don't even know if such an illegitimate entity can send such a letter to a United Nations body," she said.
The Ethiopian government labels the TPLF a terrorist organisation.
The UN Human Rights Council last week voted to launch an international investigation into abuses in Ethiopia, despite protests from Addis Ababa, amid warnings of looming generalised violence.
The 47-member council voted with 21 in favour, 15 opposed and 11 abstentions to order the establishment of "an international commission of human rights experts on Ethiopia" to probe a wide range of alleged violations and abuses by all sides.
The federal Ethiopian government has in recent months detained thousands, many of whom are ethnic Tigrayans, on suspicion of supporting the TPLF.
The two sides blame each other for the war.
The TPLF accuses Prime Minister Abiy Ahmed of wanting to centralise power at the expense of the regions, which he denies.
Mr Abiy, whose appointment in 2018 brought nearly three decades of TPLF dominance over Ethiopia to an end, says the TPLF wanted to hang onto central power. The Tigrayan leadership denies this.
Last Sunday, Ethiopians living in Kenya demonstrated during a protest titled #NoMore at the Ethiopian Embassy in Nairobi.
They rallied against what they said was foreign countries' meddling in Ethiopia.