Corruption scandals frequently grip Iraq, with smear and disinformation campaigns often used to settle political scores.
Sudani said the accusations were levelled at the government "in an immoral manner", adding the allegations "are baseless and I can say with absolute certainty that it is the lie of the century".
He was publicly addressing the allegations for the first time, in remarks reported by the state news agency INA.
The accusations first emerged in August, and subsequent reports by Iraqi and Arab media outlets suggested that among the victims of the alleged wiretapping were powerful members of the political class.
In particular, they pointed to members of the Coordination Framework, a pro-Iran Shiite parliamentary bloc that brought Sudani to power.
Iraq's judiciary has opened an investigation into the accusations, but has not publicly commented on them or revealed who is implicated.
The only individual named in the case is Mohamed al-Jouhi, a former official in Sudani's office.
The first official to publicly comment on the accusations was MP Mustafa Sanad, who alleged in August that he himself had been a victim of the wiretapping and said a network had been arrested, including officers and officials, notably Jouhi.
And in September, former speaker of parliament Mohammed al-Halbussi also claimed in a televised interview that his movements have been subject to "surveillance".
In September, the Supreme Council of the Judiciary denounced "the inaccuracy of information" circulating in the media over an investigation into the "Mohamed al-Jouhi network".
It described as "false" reports "circulating in the media and on social media regarding attempts to eavesdrop on the president" of the council, Faiq Zidan.
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