Mr Muscat declined to make a link with Caruana Galizia's 2017 murder, saying in a televised address that he was resigning "as this is what needs to be done".
"They're asking people to believe this shit", Caruana Galizia's son, Matthew, said on the Schembri vindication over the weekend.
Muscat contended that "justice is being done". Shortly after the blast, three men were arrested for allegedly carrying out the actual bombing.
The case has put intense pressure on Muscat and the Times of Maltareported on Friday that the prime minister planned to resign.
Critics including members of Caruana Galizia's family have accused Muscat, 45, of protecting those involved in murdering the popular journalist and blogger who exposed cronyism and sleaze within the tiny country's political and business elite.
Magistrate Audrey Demicoli asked Fenech to enter pleas.
Fenech had named Schembri, along with two ministers in the government, in a criminal probe into Caruana Galizia's murder.
Both men resigned on Tuesday and Mr Schembri was interrogated for two days by police before being released without charge. The investigation into her death has drawn global attention to the small Mediterranean island nation. On Thursday, Reuters published an exclusive report on a "previously untold account of the plot to kill Daphne, a contract killing that earned the killers just 150,000 euros".
"The sensations of genuine sadness and anger for this murder are justified".
The announcement followed a meeting of the parliamentary party at Girgenti, the prime minister's summer residence, which ended with a statement from Labour MPs expressing their "unanimous" support for Muscat and for the decisions he would be taking.
Muscat used his speech to praise his tenure's achievements, including strong economic growth and civil rights, including legalized marriage and adoption for same-sex couples. "This case can not define everything that our country is and what we have accomplished together", he said. His bid for immunity was rejected first by Mr Muscat on his own and later by Mr Muscat's cabinet.
Opposition leader Adrian Delia said his party would not participate in any events at which Muscat is present.
Fenech, who is suspected to be the mastermind in the Caruana Galizia assassination, had filed a warrant of prohibitory injunction seeking the removal of Arnaud from the investigation. His Labour Party had been expected to hold a leadership election in January.
According to Reuters, Vince Muscat "revealed these sensational details to the police in April 2018, in the hope of getting a pardon", which the prime minister has so far refused.