A senior European monitor is calling for Malta’s prime minister to distance himself from the investigation into the killing of the prominent investigative journalist Daphne Caruana Galizia due to a potential conflict of interest.

Malta’s prime minister, Joseph Muscat, has the power to grant immunity from prosecution to a key witness who may have vital evidence about those who commissioned Caruana Galizia’s assassination two years ago.

However, two current members of Muscat’s government have been linked to a businessman arrested on Wednesday in connection with the killing.

“The suspicions of personal and political interest are too strong, and the potential influence of the prime minister of Malta on the criminal justice system is too great,” said Pieter Omtzigt, a special rapporteur appointed by the Council of Europe to monitor events in Malta.

His comments came as businessman Yorgen Fenech was first released on police bail, and then re-arrested, giving police a further 48 hours in which to charge him. Fenech, who resigned as head of his family business last week, was apprehended while sailing away from Malta aboard his luxury yacht at around 5.30am on Wednesday morning.

Just before her death, the journalist received a massive leak of data from an energy company co-owned by Fenech.

Joseph Muscat makes a statement to media on the investigation. Photograph: Guglielmo Mangiapane/Reuters

The prime minister has taken a high-profile role in managing communications, making daily on-camera statements to the press since an apparent breakthrough in the case earlier this week.

On Tuesday Muscat revealed he was prepared to seek a presidential pardon for a key witness, Melvin Theuma, who claims to have acted as a middleman between those who planted the car bomb that killed Caruana Galizia in 2017 and those who masterminded the killing. Muscat said his decision to grant the pardon would be conditional on the evidence given by Theuma.

However, Omtzigt has joined the journalist’s family in voicing concerns that Muscat is conflicted.

Investigations have revealed Fenech as the owner of a secretive offshore company, 17 Black, which Caruana Galizia was looking into at the time of her death. It was later revealed 17 Black was due to make payments to other offshore companies belonging to Konrad Mizzi, Malta’s then energy minister, now in charge of tourism, and Keith Schembri, Muscat’s current chief of staff.

Schembri and Mizzi have both previously said they had no knowledge of any connection between 17 Black and Fenech, or of any plan to receive payments connected to Fenech.

“Concerned by events in Malta,” Omtzigt wrote on Twitter. “Who runs the investigation: PM Muscat? Who determines whether Theuma’s evidence justifies a pardon: the PM?”. He added: “Given his associations, shouldn’t PM Muscat be keeping his distance from all of this?”

Caruana Galizia’s family have issued a statement urging Muscat to step back. They said: “The prime minister has no place anywhere near the investigation and we trust that he will now distance himself from it. We are prepared to use all legal means at our disposal to ensure that the investigation is independent and impartial, and that it runs its full course.”