The Times of Malta and other local media reported on Friday afternoon, local time, that Mr. Muscat had told the president of Malta, George Vella, that he meant to step down immediately, paving the way for a leadership contest.
After two years of stalled investigations, the authorities have moved rapidly in recent days in the case of Caruana Galizia, who was blown up with a vehicle bomb while working on reports about official corruption.
A scandal around the killing of journalist and anti-corruption campaigner Daphne Caruana Galizia brought renewed protests outside Malta's parliament on Monday, November 25, with Prime Minister Joseph Muscat jeered as he left the building.
The family of the slain journalist, Daphne Caruana Galizia, said in a tweet that "we share Malta's shock and anger" that the ex-aide was released from jail a day earlier.
Schembri has served as Muscat's chief of staff since 2013.
Fenech, who was arrested on his yacht last week, has requested immunity to reveal what he knows about the case.
Muscat on Friday described the investigation as "the biggest our country has seen", but contended that no politicians were tied to the journalist's murder.
Muscat said he had recused himself from the decision over Fenech, since the suspect under police interrogation had identified Schembri as the mastermind behind Caruana Galizia's killing, according to sources.
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The Malta Today newspaper reminds that the police briefly questioned Cardona on Saturday, just a few days after Fenech's arrest.
He also refused to pardon Fenech in return for his testimony, prompting Fenech's lawyers to join the MEPs in casting doubt on his impartiality.
A person holds a candle in front of a picture of anti-corruption journalist Daphne Caruana Galizia in Valletta, Malta, October 16, 2019.
"The [Maltese] secret services are under direct control of the prime minister, so what precautions are being taken [to stop abuse]?", Pieter Omtzigt, a Dutch MP, told EUobserver. He was summoned by police for questioning last Saturday.
Mr Mizzi resigned on Tuesday and Mr Cardona has "suspended himself" from his duties.
Both Mr Mizzi and Mr Cardona denied any involvement in the death of Ms Caruana Galizia, who was killed in a auto bomb.
Leaked emails revealed in court appeared to show both politicians stood to receive payments from a Dubai company called 17 Black, owned by Fenech. The failure to prosecute Schembri, Mizzi and their protectors had fatal consequences for our wife and mother.
Similar allegations were made by a key source in the case, the taxi driver and alleged intermediary between those who commissioned the murder and the killers, Melvin Melvin Theuma. This was followed by the resignations of Tourism Minister Konrad Mizzi and Economy Minister, Chris Cardona.
Caruana Galizia's family said Muscat should not preside over an investigation that implicates three of his closest colleagues. The company belonged to Fenech, the businessman.