In a statement by his spokesperson Stephane Dujarric, Guterres urged all parties to "cease hostilities immediately" and "return to dialogue under the framework of the Pretoria Agreement," Anadolu Agency reported.
The UN chief warned against "the risks of escalation that further undermines the stability of the region."
He is "further concerned by reports of the presence of Eritrean forces in Ethiopia," according to the statement.
Guterres reminded all states in the region of their obligation under the UN Charter "to refrain from the threat or use of force against the territorial integrity or political independence of any State," as well as the principle of non-interference in internal affairs.
He urged states with influence on the parties to "use it to support de-escalation and to refrain from any action that could fuel the conflict."
"He stands ready to offer his good offices," it added.
Ethiopia and Eritrea fought alongside each other during the 2020-2022 Tigray war. But relations have since deteriorated sharply, with the governments accusing the other of threatening regional stability.
Tensions have also intensified because of Ethiopia's pursuit of access to the Red Sea, particularly the Eritrean port of Assab, which Asmara maintains is part of its sovereign territory.