The prime minister's chief of staff and other prominent political figures have also been questioned by the police regarding complicity in the murder of Caruana Galizia.
But some want Muscat to leave office now, and up to 4,000 demonstrators gathered near parliament's entrance Monday.
Caruana Galizia had alleged that Egrant, a shell company listed in the Panama Papers, was used to receive money from the family of Azerbaijan's President Ilham Aliyev. Maltese Prime Minister Joseph Muscat said Sunday Dec. 1, 2019, that he would resign in January following pressure from citizens for the truth about the 2017 auto bombing that killed a journalist.
Despite the journalist's revelations of corruption in the Maltese government, Muscat's Labour Party won the June 2017 general elections by a landslide.
Malta's prime minister since 2013, he has been criticised by opposition politicians for allowing Schembri and Mizzi to stay in their posts. The gambling tycoon is linked to prime minister Muscat's former chief of staff. Daphne Caruana Galizia's murder has rocked Malta, where thousands of have taken to the streets to demand justice and accountability.
Muscat said his reason for stepping down was that "this is what needs to be done", declining to make a direct link to his decision and the murder probe.
It followed another night of protests in front of parliament on Monday night, where citizens were blocked off Freedom Square in front of the parliament building.
"The case showed that Malta's institutions work and everyone is equal before the law", he said.
Fenech had named Schembri, along with two ministers in the government, in a criminal probe into Caruana Galizia's murder.
The government has rejected his bid for a pardon. Schembri has said he is innocent of any wrongdoing.
The integrity of the investigation had suffered serious prejudice by the fact that he had practically been forced to ask the Prime Minister for the opportunity to testify against one of his closest aides, and one he had chosen, appointed and defended for many years.
Caruana Galizia, a mother of three described as a "one-woman WikiLeaks", was blown up in a auto bomb attack near her home in October 2017.
In a packed schedule for a two-day visit, MEPs will be meeting government officials as well as the Attorney General, the Police Commissioner and investigators assigned to the investigation into the journalist's assassination.
Caruana Galizia was killed when a bomb exploded in her rental vehicle on 16 October 2017 outside her home in Bidnija.
Fenech, arrested as he tried to flee the island on his yacht, has claimed Muscat's former chief-of-staff Schembri was the "real mastermind" behind the killing, according to police sources. Schembri was arrested on 26 November and released on 28 November.