"We are fighting a defensive war," TPLF spokesman Getachew Reda said at a press conference broadcast online by the local Tigray TV channel, adding: "We will remain open for any negotiations."
Local residents as well as diplomatic and humanitarian sources have said that in recent days TPLF fighters have pushed about 50 kilometers south of Tigray into Amhara as well as to the southeast into Afar.
"We have defended our positions and we are now launching a counter-offensive," Getachew said.
The government of Prime Minister Abiy Ahmed and the Tigray People's Liberation Front (TPLF) have each blamed the other for unleashing the renewed hostilities in an area of the Amhara region just to the south of rebel-held Tigray.
"Abiy keeps making miscalculation after miscalculation, he keeps sending reinforcements and we'll continue to neutralise (them) and that will take us probably deeper and deeper into Amhara region."
In response to Getachew's comments, the Government Communication Service said: "The federal government is still committed to the peaceful resolution to the conflict that was once again initiated by the TPLF terrorist group."
Abiy's government announced Saturday that federal forces had pulled back from the town of Kobo, while Getachew said a "significant" part of the North Wollo zone in Amhara was in rebel hands.
The renewed fighting shattered a truce announced in late March and has cast a shadow over international efforts to try to end the near 22-month conflict.
The war has killed untold numbers of civilians and left millions in need of humanitarian aid, with Tigray itself without access to basic services and struggling with food and fuel shortages.
Abiy, a Nobel Peace laureate, sent troops into Tigray to topple the TPLF in response to what he said were rebel attacks on federal army camps.
The TPLF mounted a comeback, recapturing most of Tigray in June 2021 and expanding into Afar and Amhara, before the fighting reached a stalemate.
Access to northern Ethiopia is severely restricted and it is not possible to independently verify the situation on the ground or the claims by the warring sides.