Sudan and Egypt have long disputed ownership of the Halayeb and Shalatin areas between the countries near to the Red Sea.
"Sudan calls on its brothers in the Arab Republic of Egypt to sit for direct negotiations to solve this issue, as was done with the brothers in Saudi Arabia or by resorting to international arbitration," Sudan's foreign ministry said in a statement issued yesterday.
It was the first time Sudan's foreign ministry has called for talks on the small territories since Egypt transferred control of two islands in the Straits of Tiran to Saudi Arabia last Monday.
Khartoum has regularly protested at Egypt's administration of Halayeb and Shalatin, which it has said are part of its sovereign territory since shortly after its independence in 1956.