A media report published at the weekend alleged that more than 30 politicians, journalists and business executives had been targeted by state surveillance.
Pressure has mounted on the Greek government after the main opposition party Syriza demanded an explanation for a snowballing wire-tapping scandal and threatened to mount a no-confidence motion.
Syriza said on Monday it was considering tabling a motion of no-confidence.
"All options are now on the table. We will use them at an opportune moment," Syriza said.
The challenge follows a bombshell media report at the weekend which alleged that more than 30 politicians, journalists and business executives had been targeted by state surveillance.
The Supreme Court has ordered an investigation.
"The government should shed light on this affair before the next election," due in the summer of next year, the far-left party of former prime minister Alexis Tsipras said.
Weekly newspaper Documento reported on Saturday that the mobile phones of 33 high-profile public figures had been targeted illegally by spyware known as Predator and technology employed by state intelligence agency EYP.
The list of reported targets includes former premier Antonis Samaras, several serving cabinet ministers and shipping magnate Vangelis Marinakis, the owner of Olympiakos and Nottingham Forest football clubs.
Influential members of Prime Minister Kyriakos Mitsotakis's New Democracy party, who are potential rivals in any future leadership contest, were also allegedly wiretapped.
The spokesman for the government said there were "no elements of proof" to support Documento's revelations.
The scandal broke in July when Nikos Androulakis – an MEP and leader of the Socialist party (PASOK) – filed a complaint over alleged attempts to tap his mobile phone using Predator spyware.
Within days, it emerged that Androulakis was kept under surveillance separately by the national spy agency before he became leader of PASOK, the country's third-largest party.
Two journalists and another senior opposition politician also claim to have been spied on.
The scandal forced the resignations in August of the intelligence agency boss, and of a close aide and nephew to the prime minister.
The government has flatly denied using illegal surveillance software. But it has admitted the state intelligence service monitored Androulakis, without saying why.
Mitsotakis has pledged to bring in a law banning the sale of malevolent spyware.
But critics note that one of his first acts when he became prime minister in 2019 was to attach the national intelligence service to his personal office.
On Friday, a European Parliament committee investigating wiretaps in Greece and other European Union states called for a more thorough investigation.
Its preliminary report is due out on Tuesday.