Eighteen Sudanese were killed on Thursday evening in an ambush by an armed Chadian group, Sudan's state news agency (SUNA) reported on Friday.
A number of people were injured in the attack that took place in West Darfur.
Deputy head of Sudan's sovereign council Mohamed Hamdan Dagalo asked citizens to exercise self-restraint and confirmed that the authorities will take all necessary measures, SUNA added.
Dagalo was on an official visit to Chad when the attack happened.
He condemned it as a flagrant violation of Sudan’s border and sovereignty.
He took part in the funeral for the victims in al-Geneina town, the capital of West Darfur.
He noted that this was not the first attack on Sudanese civilians on their side of the border with Chad.
Dagalo added that he had called on head of the transitional council, Abdul Fattah al-Burhan, to hold an emergency security and defense council meeting and to take the necessary measures to address the situation on the border.
He stressed that the protection of civilians and the border was the responsibility of the state.
During his visit to Chad on Thursday, Dagalo met with President Mahamat Déby for talks on the border tensions.
They agreed to set radical solutions to the problems on the border.