"Seven people are known to have died in the crash," the source said.
Egyptian authorities earlier said six Russian tourists had been killed and 17 injured.
A total of 26 people, including 22 Russian tourists were on board the bus, which overturned late on Monday some 15 km (9 miles) from the Egyptian city of Dahab.
The Al-Ahram weekly wrote citing local safety authorities that the bus crash was caused by reckless driving.
"The bus overturned 15 km from the city of Dahab as it was being driven at reckless speed on a dangerous mountainous road," the newspaper wrote.
Prosecutors in Egypt's South Sinai region have started an accident investigation into the fatal crash.
All of the injured have been taken to an international hospital in Sharm-El-Sheikh where they are receiving medical treatment.
Road accidents are frequent in Egypt largely due to reckless driving and poor roads. According to the Egyptian Interior Ministry, about 27,000 road accidents occur in the North African country every year, killing over 6,000 people and injuring another 30,000.
According to data provided by Russian travel agencies, Russian tourists are most commonly killed and injured in fatal road accidents in Ukraine, Turkey and Egypt.
Last week at least 24 Russian tourists were killed and 25 injured in a fatal road accident in Israel caused by reckless driving after a bus plunged 80 meters (263 feet) down a ravine near the Red Sea resort city of Eilat.
