ADDIS ABABA, Ethiopia — President Salva Kiir of South Sudan and the rebel commander Riek Machar signed another cease-fire agreement on Monday, edging them closer to a final deal to end a 15-month conflict that has ravaged the new country, mediators said.

African diplomatic sources said the agreement, which was not immediately made public, sets out how the two leaders would share power once they formed an interim government. It proposes that Mr. Kiir would remain president while Mr. Machar would become vice president, the sources said.

The warring sides also agreed to abide by a cease-fire deal that was signed in January 2013, but which has been frequently violated.

The rebels, however, said many more details need to be agreed upon before the deal could be labeled a “power sharing” agreement.