For the first time, Mexico’s President Enrique Peña Nieto has acknowledged that his government had purchased spying software.
A report in last Monday's New York Times says the system has been used to spy on human rights activists, lawyers and journalists.
The Mexican Digital Rights Defense Network says 88 cases have been recorded.
But the government denies using the software for espionage purposes.
At a news conference, Peña Nieto said the Israeli-made system, called Pegasus, had been bought by his administration.
The software can hack into mobile phones and is designed to be used against security threats.
He promised an investigation into any misuse and then added: “And I hope, under the law, it can be applied against those that have raised false accusations against the government...This government categorically rejects any kind of intervention in the private life of any citizen".
The immediate response, in particular of victims of the hacking attempts, was shock.
“This not the expected behavior of the head of state of a young democracy,” said Juan Pardinas, the head of the Mexican Institute for Competitiveness, who was the victim of a hacking attempt. “This is the statement of an apprentice of Vladimir Putin.”
Peña Nieto later elaborated on his comments. “What I said, the scope of the instruction I gave, was precisely to follow up on the criminal complaints that some activists have filed regarding this supposed spying".
Mexico's Digital Rights Defense Network also said it had found evidence to back up the 88 claims it revealed earlier this week.
In each case, the targets received a text message on a smartphone that when clicked installed the spyware on the device.
The software gives the attacker access to all the phone’s files as well as the ability to control the camera and microphone.
On Wednesday, the Mexican attorney general's office said prosecutors would investigate the origin of the fake messages as well as the supplier of the spyware.