The summit aims to "develop effective mechanisms" with neighbouring states to settle the conflict peacefully, in coordination with other regional or international efforts, the presidency said in a statement.
The fighting that erupted on April 15 in the Sudanese capital Khartoum has driven more than 2.9 million people from their homes, including almost 700,000 who have fled to neighbouring countries.
Over 255,000 have crossed into Egypt, according to latest figures from the International Organization for Migration.
Egypt has close ties to Sudan's army, which has been battling the paramilitary Rapid Support Forces in Khartoum and other parts of Sudan.
Egypt was not involved in talks in Jeddah led by the United States and Saudi Arabia that were adjourned last month after failing to secure a lasting ceasefire.
