The Mexicans have said their tour group came under aerial attack on Sunday in what the Egyptian interior ministry described as a botched operation against militants in the Western Desert. Four Egyptians were also killed.
Foreign Minister Claudia Ruiz Massieu arrived in Cairo early on Wednesday seeking answers from the Egyptian government, after President Enrique Pena Nieto expressed his country's "outrage".
She told reporters at the Dar Al Fouad hospital that the condition of the survivors was "stable" and they were "increasingly better".
"We expect an exhaustive and complete and comprehensive and transparent investigation," Ruiz Massieu said.
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The Egyptian government has said guides took the tourists into a restricted zone, an accusation vehemently denied by a union representing the guides.
In a letter addressed to Mexicans on Tuesday, Egyptian Foreign Minister Sameh Shoukry expressed his "deepest condolences" for the incident.
But he stopped short of an apology, saying there was a probe under way and that "the chain of events is still confusing and unclear".
Sisi called Pena Nieto on Tuesday to express his "most sincere condolences" over the "tragic incident," the Mexican leader's office said in a statement.
His foreign minister, accompanied by relatives of four the victims, will try "to obtain first-hand information that would clarify the circumstances of this deplorable event," a statement from her ministry said.
In Mexico, details of the victims began to emerge from families and friends.
They reportedly included 41-year-old musician Rafael Bejarano Rangel, whose mother was wounded in the strike, as well as former university professor Luis Barajas Fernandez and model agency head Queta Rojas.
Egypt said the tourists entered a restricted area in the Western Desert and were "mistakenly" killed as security forces chased jihadists who had abducted and beheaded an Egyptian.