"The incident resulted in the death of 12 Mexicans and Egyptians and the injury of 10 others who have been transferred to hospitals."
Rasha Azazi, spokesperson for the Egyptian Ministry of Tourism, said the tourists were taking part in an unapproved safari at an off-limits site using unlicensed cars.
She said trips to the Farafra area are meant to be cleared by officials but that the group "did not have permits and did not inform authorities".
Mexico`s foreign ministry confirmed that two of the dead are from Mexico, but they are yet to be officially identified.
Work is also underway to identify the other victims.
Jorge Alvarez Fuentes, Mexico`s ambassador to Egypt, has been at a Cairo hospital where he met five Mexican survivors who were in a stable condition.
Mexican President Enrique Pena Nieto condemned the attack on his Twitter account, describing it as a tragic incident.
He has demanded a full investigation.
Egypt has battled an Islamic insurgency by an affiliate of the so-called Islamic State in northern Sinai for many years and this has killed hundreds of soldiers and police.
The attacks spread to the mainland and started to attack tourist targets after the ousting of Islamist president Mohammed Morsi in July 2013.
Egyptian officials say militants across Libya and the west of Egypt have been trying to connect with Islamists in the Sinai region.
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