According to the left-leaning weekly Documento, the list of targets includes Olympiakos and Nottingham Forest football club owner and former prime Antonis Samaras, as well as current cabinet members and shipping tycoon Vangelis Marinakis.
According to the publication, illegal software called Predator was used in conjunction with equipment utilised by Greece's national spy agency, EYP.
Influential New Democracy party members who might challenge Prime Minister Kyriakos Mitsotakis for the leadership in the future were among those targeted, according to the publication.
"The evidence is missing," said government spokesman Giannis Oikonomou, who nonetheless called on judicial authorities to investigate what the newspaper has reported.
He accused the report of trying to "hurt" the government and undermine stability.
The weekly, which has close links to the main opposition Syriza party, sourced its information to "two people with key roles in the surveillance" and said illegal software was also used to tap mobile phones.
On Friday, a European Parliament committee investigating wiretaps in Greece and other EU states called for a deeper investigation of the case.
A Greek parliamentary committee set up to investigate the scandal folded after a month, and critics said it failed to summon key witnesses.
The affair exploded in July when Nikos Androulakis -- an MEP and leader of Greece's Socialist party -- filed a complaint against alleged attempts to tap his mobile phone using Predator spyware.
Within days, it emerged that Androulakis under surveillance separately by Greek intelligence before he became leader of Pasok, the country's third largest party.
Two Greek journalists and another senior opposition politician also claim to have been under surveillance.
The scandal forced the resignations in August of the Greek intelligence service chief as well as a close aide and nephew to the prime minister.
The Greek government has flatly denied using illegal surveillance software. It has admitted that state intelligence monitored Androulakis, without disclosing the reason.
"Surveillance software exists in Greece as in the rest of Europe, but no (Greek) public authority has purchased or uses it," Oikonomou said Saturday.
Mitsotakis has promised to ban the use of illegal wiretaps by law.
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