The group has pressed charges with the attorney general's office, accusing the government of illegally accessing private communications and other offenses, it announced at a press conference.
The nine plaintiffs at the press conference on Monday included journalists who have published embarrassing exposes on government corruption and activists who have investigated human rights violations by the state.
"This is an operation by the Mexican state, in which state agents -- far from doing what they should legally do -- have used our resources, our taxes, our money to commit serious abuses," said journalist Carmen Aristegui.
Aristegui, a well-known reporter, is known in Mexico for a 2014 expose revealing that President Enrique Pena Nieto's wife had bought a $7 million Mexico City mansion from a government contractor.
She is among the 76 cases the plaintiffs say they have documented of high-tech spyware being installed on their phones and those of their families and associates.
"What does the Mexican president have to say today about this treacherous, illegal spying?" Aristegui said.
Victims said they received text messages with eye-catching news headlines, social media posts or even communications from the United States embassy -- all of which were fake.
The messages would prompt users to click on a link that would secretly install the spyware on their phones.
The software in question, known as Pegasus, effectively turns a target's cell phone into a pocket spy, accessing the user's communications, camera and microphone to enable a highly detailed level of surveillance.
The accusation came as The New York Times published a report detailing how Pegasus was used against top human rights lawyers, journalists and anti-corruption activists in Mexico.
The spyware is made by a secretive Israeli firm called NSO Group, owned by US private equity firm Francisco Partners Management.
According to the Times report, at least three Mexican federal agencies have purchased some $80 million of spyware from NSO Group since 2011.
The company, which claims it only sells Pegasus to governments, says it has an agreement with clients that the software be used only to target terrorists and criminals.
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