JERUSALEM — The intensifying scrutiny of NSO Group, the Israeli spyware firm, has largely come from overseas as evidence mounted that authoritarian governments had used NSO products to spy on political opponents.

On Monday, the controversy came home as the Israeli government said it would investigate reports that the Israeli police had illegally used spyware against its citizens without a court order, including a key state witness in the corruption trial of former Prime Minister Benjamin Netanyahu.

Prime Minister Naftali Bennett, who succeeded Mr. Netanyahu last June, said the deputy attorney general was “looking quickly into” the claims, while the public security minister, Omer Barlev, who oversees the police, said he would open an official inquiry.

The efforts constitute the Israeli government’s most public expression of concern about NSO — once promoted by Israeli officials as a centerpiece of the Israeli tech industry — since the firm began attracting global scrutiny in 2016.

The allegations caused a brief delay in Mr. Netanyahu’s trial, after judges postponed hearings on Monday to allow prosecutors time to address the claims, amid calls by Mr. Netanyahu’s allies for the trial to be scrapped entirely.

The moves reflected rising concerns within Israel about the use of spyware made by NSO and other companies, which had been spared significant domestic scrutiny because it was not widely seen as a threat to Israeli citizens.

But on Monday NSO’s flagship spyware product, Pegasus, was being portrayed in Israel in much the same way it has been by critics abroad, as a threat to democracy.

Mr. Bennett said that “the reports about Pegasus, if they are true, are very serious.” Spyware products like Pegasus, he added, “are important tools in the fight against terrorism and severe crime, but they were not intended to be used in phishing campaigns targeting the Israeli public or officials — which is why we need to understand exactly what happened.”

Created to help governments track criminal and terrorist activity, Pegasus allows its users to monitor every aspect of a target’s phone — including their calls, messages, photos and video. In Israel it cannot legally be used against Israeli citizens without a judicial warrant.

Ayelet Shaked, one of several cabinet ministers to speak about the furor, described the allegations as “an earth