Gilf al-Kebir is a remote plateau near the Libyan border
Eleven European tourists have been kidnapped along with eight Egyptians while making an off-road tour of southern Egypt.
Five Italians, five Germans and a Romanian were taken along with eight Egyptian travel guides and drivers.
Reports said the abduction, near the Gilf al-Kebir plateau, was carried out on Friday by tribesmen or bandits.
Egypt's tourism minister, Zoheir Garana, said a ransom had been demanded and negotiations were under way.
A ministry statement said: "This is an act of banditry not of terrorism."
Minister Garana told Associated Press news agency that a ransom of up to $6m (£3.24m) had been demanded.
He says the tourists are believed to have been taken across the border into Sudan.
Egypt's tourism minister on the abduction
"According to the information we have, the hostages are in Sudanese territory but we don't know where," Mr Garana said.
Kidnappings of foreigners in Egypt have been very uncommon in recent years.
But BBC Arab affairs analyst Magdi Abdelhadi says an incident like this could dent Egypt's reputation as a safe destination for foreign tourists and deliver a blow to an industry that brings in $8bn a year.
The tourism ministry said those abducted along with the foreigners were two guides, four drivers, a guard and the owner of the travel company who had organised the trip to Gilf al-Kebir, near the Libyan and Sudanese borders.
Gilf al-Kebir is a giant plateau famous for its prehistoric cave paintings, which featured in the 1996 film The English Patient.
Local tourist guides inside southern Egypt told news agencies that the tourists were travelling in three or four off-road vehicles.
The Egyptian Mena news agency reported that the tour company owner had called his wife on a satellite phone to say the group had been kidnapped by five masked men speaking English "with an African accent".
The BBC's Ian Pannell in Cairo says local guides have indicated that the Gilf al-Kebir area has become increasingly unsafe this year.
Another group of foreigners was held at gunpoint in February and three of their vehicles were taken.
An investigation at the time pointed the blame at smugglers and bandits.
Our correspondent says there has been criticism that the Egyptian military has not done enough to patrol the area despite the increased threat.
The German and Italian foreign ministries confirmed that five nationals from each of their countries were among the group.
Both said they had set up crisis teams to deal with the incident.
There were initially reports that the group included Israeli tourists. But Israelis were not mentioned in later reports, and the Israeli foreign ministry denied any of its nationals were involved.
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