Earlier local officials confirmed that three citizens from Ukraine, Romania and Egypt had died. Some 28 others, including 16 Russians, four Egyptians, two Canadians, two Italians, two Romanians, a Briton and a Ukrainian, were injured in the accident.
The vehicle, carrying 37 tourists from the popular tourist resort of Sharm el-Sheikh to the Egyptian capital, Cairo, hit a sharp bend on a desert highway at Abu Zenima, about 40 miles (65 kms) southeast of the Suez Canal.
Most passengers were asleep when the accident occurred.
A special commission has been established to investigate the circumstances of the accident, which some media sources reported was due to a burst tire.
Such incidents are frequent on Egyptian roads due to a combination of speeding and the poor condition of the roads. Some 8,000 people die annually each year in the country in road accidents.
Egypt is a popular tourist destination among Russians with some 1.5 million people visiting the country from Russia last year.