Sudanese President Omar al-Bashir pulled out of the conference in Ethiopia after South Sudan seized Heglig, a small town in an oil field, Voice of America reported.
African officials had hoped a sidelines meeting between Bashir and Salva Kiir, president of South Sudan, at the Tana High-Level Security Forum would defuse the border crisis.
South Sudanese leaders said Saturday they had beaten back a Sudanese force trying to retake Heglig. South Sudan carried out its raid Tuesday.
Alfred Taban, editor of The Juba Monitor in the South Sudan capital, said full-scale war seemed likely.
"The city is on a war footing," he said. "There are demonstrations being held every day and the youths are going to the headquarters of the Sudanese People's Liberation Army to register in order to go to the frontline."
The crisis is expected to be a major topic at the Tana conference.
South Sudan became an independent country less than a year ago.