Ethiopian Prime Minister Abiy Ahmed (L) and Sudan leader Abdel Fattah al-Burhan, Nairobi, Kenya.
Their talks follow a clash on their tense border last month in which Khartoum said that Ethiopian forces had captured and killed Sudanese troops -- claims denied by Addis Ababa.
"We have both agreed that our two countries have plenty of collaborative elements to work on peacefully," Abiy said in a Twitter post, accompanied by a picture of the two men.
"Our common bonds surpass any divisions. We both made a commitment for dialogue & peaceful resolution to outstanding issues," he said.
Both leaders were in the Kenyan capital for a summit of the Intergovernmental Authority on Development (IGAD) regional body.
Sudan's ruling sovereign council said only that there had been a "closed-door meeting" between Burhan and Abiy.