Salman and Sisi are among 15 leaders attending the Arab League summit in Sweimeh on the Dead Sea coast to discuss regional conflicts.
Aramco had halted agreed monthly deliveries of 700,000 tonnes of petroleum products without explanation.
The move was announced after Egypt voted in favour of a Russian-drafted UN Security Council resolution on Syria that Saudi Arabia strongly opposed.
An agreement to hand over to Saudi Arabia two Red Sea islands in the Straits of Tiran, signed during a visit by Salman to Cairo last April, had also foundered on a court ruling that blocked the move.
An Egyptian presidency statement said the two leaders "stressed the importance of pushing forward and developing bilateral relations in all fields" in Wednesday's meeting.
"King Salman invited the president to an official visit to the kingdom, which was welcomed by" Sisi, the presidency said, adding that Sisi also invited Salman to visit Cairo.
Saudi Arabia supported Egypt with billions of dollars in aid after Sisi, who was the army chief, toppled Islamist president Mohamed Morsi in 2013.
Saudi Arabia views the political Islamism of Morsi's Muslim Brotherhood with suspicion.
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Aramco had halted agreed monthly deliveries of 700,000 tonnes of petroleum products without explanation.
The move was announced after Egypt voted in favour of a Russian-drafted UN Security Council resolution on Syria that Saudi Arabia strongly opposed.
An agreement to hand over to Saudi Arabia two Red Sea islands in the Straits of Tiran, signed during a visit by Salman to Cairo last April, had also foundered on a court ruling that blocked the move.
An Egyptian presidency statement said the two leaders "stressed the importance of pushing forward and developing bilateral relations in all fields" in Wednesday's meeting.
"King Salman invited the president to an official visit to the kingdom, which was welcomed by" Sisi, the presidency said, adding that Sisi also invited Salman to visit Cairo.
Saudi Arabia supported Egypt with billions of dollars in aid after Sisi, who was the army chief, toppled Islamist president Mohamed Morsi in 2013.
Saudi Arabia views the political Islamism of Morsi's Muslim Brotherhood with suspicion.
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