Eritrean Foreign Minister Osman Saleh made the request in a letter to the council on Saturday, a day after Ethiopia accused Eritrea of launching an "all-out invasion" and said Eritrean troops had advanced up to 60 kilometres (37 miles) into Tigray.
Saleh said the claims of an Eritrean incursion were part of an Ethiopian plan to justify a war of aggression, and urged the UN to intervene under Chapter VII of the UN Charter, which allows measures ranging from sanctions to military action.
The two neighbours have accused each other of starting a war over Tigray, where Ethiopia says Eritrea is backing rebel forces. An alliance of seven armed groups launched attacks against federal troops in the northern region last month in an effort to overthrow Prime Minister Abiy Ahmed's government. Eritrean forces have reportedly entered Ethiopian territory, and Addis Ababa accuses Asmara of backing the rebel Tigray People's Liberation Front (TPLF).
Ethiopian forces pushed TPLF fighters back this week and seized the regional capital, Mekelle. Ethiopia also said it had carried out drone strikes against Eritrean troops in the region.
"Eritrea requests the UN Security Council to forcefully condemn Ethiopia's deplorable declaration of war against Eritrea ... and take the requisite deterrent measures," Saleh wrote. He warned that Ethiopia's action would cause "huge devastation to the peoples of both countries and destabilise the whole region".
Ethiopian Foreign Minister Gedion Timothewos, in a letter to the council on Friday, accused Eritrea of "a blatant act of aggression that engages Ethiopia's inherent right to self-defence". He invoked Ethiopia's right to self-defence under Article 51 of the UN Charter.