(CNN) Egyptian security forces killed 12 people and injured 10 more after firing upon a tourist group they had mistaken for militants, the country's Interior Ministry said.

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."

Mexican condemnation

Two of those killed and at least six of the injured were Mexicans, said Mexican Foreign Minister Claudia Ruiz Massieu.

Six other Mexicans who were listed as being among the tour group are still unaccounted for, Ruiz Massieu said as she prepared to board a flight to Cairo.

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.

México condena estos hechos en contra de nuestros ciudadanos y ha exigido al gobierno de Egipto una exhaustiva investigación de lo ocurrido. — Enrique Peña Nieto (@EPN) September 14, 2015

Nieto has called for the Mexican Embassy to increase staff to help victims and their families.

Ruiz Massieu has contacted Egypt's ambassador to Mexico, Yasser Shaban, and "demanded a quick, exhaustive and thorough investigation and an objective explanation, without delay, so that the facts are clarified and responsibilities established," a statement said.

Shaban said the Egyptian government was taking the incident seriously and working around the clock to provide support and assistance to the victims and their families.

"Allow me at the beginning to express on behalf of the Egyptian government and people our deepest and heartfelt condolences to the Mexican government and the Mexican people and especially to the grieving families who lost their loved ones in this tragic event," he told reporters Monday.

"Our hearts ache with sorrow," he said.

Tourism and militants

A relative of one of the Egyptian victims also spoke out, calling for an immediate investigation.

"Our blood is not cheaper than any foreigners," Amr Imam told CNN. "I think over the next few days, Egyptian authorities should have a clear and honest response."

The U.S. State Department said it was investigating reports that an American citizen was injured in the bombardment.

Egyptian state media reported that an American woman was receiving treatment at a hospital outside Cairo and had been visited by U.S. embassy staff.

Egypt's Western Desert draws tourists with spectacular landscapes such as the Great Sand Sea, which Egypt's tourism board advertises as "the world's third largest dune field." All-terrain vehicles carry sightseers up and over dunes and past rock formations whittled by eons of wind-blown sand.

Tourists stop over at oases to enjoy rich desert culture and cuisine.

But the area, which is next to Libya, has also become attractive to insurgents since the fall of Libyan leader Moammar Gadhafi in 2011.

The border became porous, allowing the unhindered transport of weapons, drugs and people to and from Egypt, according to the Washington Institute for Near East Policy , a think tank that specializes on U.S. diplomacy in the Middle East.

After Egypt's military deposed former Egyptian President Mohamed Morsy of the Muslim Brotherhood in 2013, Islamist militants stepped up attacks against military targets in the Western Desert.

A deadly attack in July 2014 on an Egyptian guard post at the oasis town of Farafra prompted the Egyptian military to launch a campaign against insurgents operating near Libya. Farafra is also a tourist destination.

El-Nahla, the union chief, questioned why the tour group's police escort would let the tourists drive into a restricted area when the escort allegedly had information on "heated events in this area in the preceding two days."

Now, "one of Egypt's best tour guides," the sole provider for his three children, has been killed as a result, El-Nahla said.

"Due to negligence and lack of coordination between the tourism and the interior ministries, Egypt and tourism will pay the price through the impact of this incident on tourism in Egypt," El-Nahla wrote. "We demand that the presidency open a thorough investigation to identify the individuals and departments responsible for this negligence."