The visit comes after Sultan Haitham visited Egypt last Sunday, where discussed with President Abdel Fattah al-Sisi "the overall regional and international developments," Oman state news agency said.
Relations between Egypt and Iran have been strained in recent decades although the two countries have maintained diplomatic contacts.
Egypt's Sunni Muslim Arab ally Saudi Arabia and Shi'ite Muslim Iran announced in March that they would restore diplomatic relations, in a deal brokered by China, after years of hostility. Both countries thanked Oman for hosting previous talks between them.
Oman has also been mediating between Saudi Arabia and the Iran-backed Houthi movement. In April, Omani and Saudi envoys held peace talks with Houthi officials in Yemen's Sanaa as Riyadh seeks a permanent ceasefire to end its military involvement in the country's long-running war.
Oman, which shares borders with Yemen, has been trying for years to bridge differences between Yemen's warring parties, and more broadly between Iran and Saudi Arabia and the United States.
