The back and forth raised new doubts about the likelihood of a solution to the mystery of how an Apache military helicopter crew could have mistaken a midday picnic in the desert for a camp of heavily armed militants. Human rights advocates charged that the Egyptian Army had often failed to distinguish civilians from combatants and had seldom sought to investigate or punish those responsible.
“We are dealing with a dreadful loss of life and an unjustified aggression,” the Mexican foreign minister, Claudia Ruiz Massieu, said late Monday before boarding a plane with the families of those killed or injured for a hastily planned trip to Cairo.
She vowed to press the Egyptian authorities “for firsthand information that clarifies the circumstances of this deplorable event that cost the lives of innocent Mexican tourists.”
In “an open letter from Egypt to the people of Mexico,” Sameh Shoukry, the Egyptian foreign minister, began by offering “deepest sympathy and condolences for the loss of innocent Mexican lives” and went on to say that his nation’s law enforcement personnel exercised caution and restraint even when their own lives were in peril.
He said that an inquiry into “what happened on that fateful day” was still underway. “The emerging facts indicate that an operation was taking place against terrorists in that area at the time the convoy passed,” he said. “We still do not know if the convoy was simply in the wrong place at the wrong time, or if some error was involved.”
“I am deeply troubled, he added, “that some people have chosen to exploit this tragic event to allege that Egyptian law enforcement officials have no strict rules of engagement, act indiscriminately, or do not take the necessary precautions during their operations.”
The critics “forget that terrorism in Egypt has targeted tourists in the most despicable of ways,” he wrote, adding that years of militant violence had made Egyptians “closest to understanding just how deep this sorrow and grief may feel.”
Earlier on Tuesday, President Abdel Fattah el-Sisi called President Enrique Peña Nieto of Mexico to express his condolences. In a statement, Mr. Peña Nieto said he had told Mr. Sisi that the episode had brought “pain and indignation” to Mexican society, and repeated his government’s call for a swift and thorough investigation.
A spokesman for Egypt’s Foreign Ministry did not return calls seeking comment. And although the helicopter that conducted the attack belonged to the military, a spokesman for the armed forces deflected responsibility on Monday. “When it comes to tourists, it is a Ministry of Interior issue, not ours,” the spokesman, Brig. Gen. Mohamed Samir, said.
Mexican officials said Tuesday that they had confirmed the deaths of eight of their citizens, up from two the previous day.
For the 14 Mexican visitors, the trip was intended to be a spiritual quest, not just a tour of ancient monuments and temples.
Among the dead was Rafael Bejarano, 41, a Reiki healer and musician, his relatives said. In /images posted on Facebook before his death, he grinned into the camera, wearing a colorful, flowing outfit and holding a small child in his arms. In a post written about a trip to the Amazon, he struck a spiritual tone. “True power comes from the heart,” he wrote. “It simply feels different than the one we use to compensate for our insecurities and weaknesses.”
Mr. Bejarano’s mother, Marisela Rangel Davalos, who was wounded, had made the trip several times with a Spanish-speaking guide, Nabil el-Tamawy, whom she had known for years, her daughter Gabriela Bejarano told the Mexican news media.
Mr. Tamawy, who was in his 50s, was also killed. His family and friends said he had loved his work but had put his family, including a son who attends Cairo University and two teenage daughters, above all. He was a fan of Cairo’s Al-Ahly soccer club, and he took special pride in becoming an expert on Egypt’s history and sharing it with tourists. “Everybody loved him,” said his son, Islam Ali, an engineering student.
The other three Egyptians who died in the airstrike appear to have been the full management of the small hotel, Qasr el Bawity, that organized the tour.
One of them was Awad Fathy, a local Bedouin who had taught himself four languages, practiced pottery and painting, and learned to work underwater as a welder on ship repairs, according to a cousin, Amr Imam, a human rights lawyer. Mr. Fathy “loved traveling and the desert, so he decided he would work as a cook on long scuba diving trips, on safaris and on camping in natural reserves,” Mr. Imam wrote on Facebook.
Human rights groups said the attack reinforced concerns about the rules of engagement used by Egyptian security forces in operations against insurgents. During a two-year campaign to crush an Islamist insurgency in the North Sinai, for example, residents and rights groups have often accused the security forces of destroying homes and killing civilians. Yet the Egyptian Army has acknowledged virtually no such collateral damage and releases only periodic tallies of the number of “terrorists” it has killed.
“This is exactly what we have documented in Sinai, so it can send a message of how the Egyptian military is dealing with the situation in Sinai and now in the Western Desert,” said Mohamed Elmessiry, a researcher on Egypt at Amnesty International.
In one case, Mr. Elmessiry said, an Apache helicopter fired three missiles at houses in Al Akour, a village in North Sinai. Two of the missiles hit houses, he said, killing at least 10 people, including a pregnant woman and children.
“They use excessive lethal force against everyone in the spots where they expect there are armed groups,” he said.
Sarah Leah Whitson, director of the Middle East and North Africa Division at Human Rights Watch, said, “The track record of the Egyptian authorities in investigating the killings of their own citizens is extremely poor, and there is absolutely no indication based on this past record that there will be any real accountability for this incident.”
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Merna Thomas contributed reporting from Cairo, and Elisabeth Malkin from Mexico City.