Israel's government will set up a commission of inquiry to examine allegations that the police used spyware to hack the phones of Israeli public figures without authorisation.

Officials, protesters, journalists and a son of former Prime Minister Benjamin Netanyahu were targeted without court orders, the newspaper Calcalist said.

A witness in Mr Netanyahu's corruption trial was also allegedly hacked.

Prime Minister Naftali Bennett said the reports were "very serious, if true".

Reports say the police used Pegasus software, developed by NSO, an Israeli surveillance firm. NSO has faced widespread allegations that the product has been sold to and misused by authoritarian governments across the world.

The company has insisted that it does not operate the software once it is sold to clients and has previously stated that it could not be used to track Israeli citizens. It has not commented on the latest development.

Pegasus infects phones, allowing operators to extract messages, photos and emails, record calls and secretly activate microphones and cameras.

"This tool (Pegasus) and similar tools, 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," Mr Bennett said in a statement.

The prime minister said Deputy Attorney General Amit Merari was looking into the matter urgently and that newly appointed attorney general, Gali Baharav-Miara, would "not leave the public without answers".

President Isaac Herzog said: "We must not lose our democracy. We must not lose our police. And we must certainly not lose public trust in them. This requires an in-depth and thorough investigation."

Public Security Minister Omer Barlev said the commission of inquiry would be headed by a retired judge and would have the power to question anyone necessary in the political, legal and security systems and seize documents.

In a report published on Monday, Israeli business daily Calcalist said police hacked the phones of dozens of Israeli citizens.

The surveillance was conducted by the force's cyber-SIGINT unit to "phish for intelligence even before any investigation had been opened against the targets, and without judicial warrants", according to the newspaper.

The list of targets allegedly included:

According to Calcalist, the hacking and collecting of information from their phones took place while the police force was led by Roni Alsheikh, who was commissioner between 2015 and 2018.

Last Wednesday, Israeli media reported that police hacked the phone of Shlomo Filber, a former director-general of the communications ministry and key witness in the ongoing trial of Mr Netanyahu on charges of bribery, fraud and breach of trust in connection with Case 4,000 and two other cases. The reports did not mention whether Pegasus was used.

Mr Netanyahu, who along with Mr Elovitch denies any wrongdoing, described those reports as "an earthquake". His lawyers were expected to request a postponement of Mr Filber's testimony, which is expected next week.

It was not immediately clear whether information obtained through the alleged hacking was being used against Mr Netanyahu, who was ousted as prime minister last June. Israeli media cited police as saying that material was not transferred by the cyber-SIGINT unit to investigators.