Sudan on Saturday summoned the Ethiopian chargé d'affaires over an alleged incursion in the eastern Gedaref State by suspected Ethiopian militia last week.
The Ministry of Foreign Affairs in a statement that it condemned the occurrence and called for a truce.
"The sustainability and progress of the co-operation between the two countries must be based on mutual respect for the sovereignty, independence and borders of each of them and the right of their peoples to live in safety and peace and to use their natural and economic resources without the encroachment or aggression of any party on the other," state news agency SUNA reported.
The cross-border incursion in al-Baraka area on Thursday led to the death of one Sudanese soldier and a child. Six other soldiers were injured, according to the Sudanese army.
This comes at a time when Khartoum and Addis Ababa are preparing for a second high-level meeting to resolve the border crisis. The meeting will be chaired by Sudanese Minister of the Cabinet Affairs Omar Manis and Ethiopian Deputy Prime Minister Abiy Ahmed.
Reacting to the development on Sunday, Ethiopia called for an amicable solution to the border tension.
"In the spirit of containing the situation on the ground and avoiding any further tension, the Ministry urges that the two countries should work together through existing military mechanisms to address and jointly investigate circumstances surrounding the incident," the Ethiopian Foreign Ministry said on Sunday.
"The Ministry strongly believes that there is no honourable reason for the two countries to descend into hostility and calls for the need to continue the close collaboration between neighbouring local and regional administrations to ensure peace and security in the border area," it added.
Gedaref State, an arable region that straddles the Sudan-Ethiopia border, has witnessed a spate of attacks in the recent past particularly during harvest seasons.
The state is divided into three regions: Grand Fashqa, Little Fashqa and the southern region.