The lifeboats were seen in waters off the Egyptian port city of Safaga, some 600 kilometers (370 miles) southeast of Cairo, security sources said. Earlier, a security source said bodies were sighted in the water.
Maritime sources said at least 1,310 Egyptians were on board, as well as around 100 people from other countries, including Sudanese and Saudi nationals.
Among the passengers were pilgrims returning from the annual Muslim hajj to Mecca, they said.
The Egyptian ship, called Al-Salam 98, had departed from the Saudi port of Duba and had been due to reach Safaga at 2:30 am local time (0030 GMT).
However, officials lost radar contact with the ship, and air and maritime rescue teams were mobilized.
The boat was also reported to be carrying more than 40 vehicles.