"They are two Frenchwomen, found shot to death in a touristy area of Salta province," Judge Martin Perez told TN television.
The bodies of the women, both 30, were spotted Friday by hikers near San Lorenzo hill, west of the provincial capital, the judge said. The hiking area popular with tourists leads to an observation point offering a panoramic view of the city and surrounding area.
"Salta needs to clear up this appalling crime immediately," Governor Juan Manuel Uturbey said at a press conference at his office.
Uturbey said the victims' identities were known but he did not immediately announce them, though police sources told El Tribuno de Salta newspaper the women were Houria Moumni and Cassandre Bouvier.
The French foreign ministry said it wanted "the crimes solved, and for those who are responsible to be identified and tried."
One was shot in the head and apparently sexually abused, her clothes torn, and the other was shot in the back, the judge said.
No arrests have been made and authorities have launched an investigation.
The women had arrived in Salta on July 11 and planned to stay through July 19, police said. They were last seen at their hotel, where they had left their backpacks, on July 16.
"There is a lapse of several days where there was no sign of what their activities were," said Marcelo Baez, a justice spokesman in Salta.
"Police are trying to put together the pieces. What is clear is that they were brutally murdered."