Members of Egypt's military and police were chasing "terrorist elements" Saturday in the country's vast Western Desert when they came upon the tourists. Among the victims were Mexicans and Egyptians, the ministry said.
The attack happened within a so-called restricted area.
The tourist group was in cars not authorized for tours, and the group did not have permits for the trip, MENA state news agency reported, citing Egypt's Ministry of Tourism.
An investigation is ongoing, but the head of the tour guides union disputed the state-run media account, saying, "The tour company is licensed. They had the tourism police notification. The police representative inspected all car licenses before leaving the hotel in Cairo in the morning and heading towards the oases."
One of the tourists was diabetic and couldn't wait until the group reached its destination to eat, the union's Hassan El-Nahla said, so the group took a 2-kilometer (1.2-mile) detour off a paved road.
"There were no warning signs and no instructions from the checkpoints on the road or the tourism policeman accompanying them," El-Nahla's statement on Facebook said. "I strongly condemn the lack of coordination between the ministry of tourism, in not following up with the events, and the police."
Two of those killed and at least six injured were Mexicans, Mexico's foreign ministry said. The government is still in the process of identifying all the victims.
The country's ambassador to Egypt, Jorge Alvarez Fuentes, spoke to the hospitalized Mexicans, "who individually told him they had suffered an aerial attack with bombs launched from an airplane and helicopters. They were evacuated by civilian and military vehicles and then transported by ambulance to the hospital."
Mexican President Enrique Peña Nieto mourned the loss of his country's citizens in posts to Twitter.
"Mexico condemns these acts against our citizens and has demanded that the Egyptian government conduct an exhaustive investigation of what happened," he said.