Caruana Galizia was killed by a vehicle bomb as she drove out of her home and three men are now awaiting trial for having set off the bomb.
Her family demanded on Friday that Muscat resign, after his right hand man Keith Schembri was set free overnight.
On Tuesday morning, November 26, Muscat announced the resignation of his chief of staff Keith Schembri.
Earlier on Friday, Muscat's cabinet turned down a request to pardon a businessman, Yorgen Fenech, over the murder in return for testimony that Fenech's lawyers said would implicate senior government figures including Schembri.
Two of the ministers had already left the cabinet this week over links to Mr Fenech as the murder case unfolded.
European Union leaders, he said, "made the mistake of embracing Muscat" because he "disguised himself as a liberal", but was actually "a populist, heavily authoritarian; his government is extremely corrupt". Mizzi, who resigned on Tuesday, said he had not committed any crime but was leaving "in light of political, extraordinary and general circumstances in the country".
The investigation has led to renewed calls by opposition politicians for Muscat to resign.
On Friday evening, Muscat issued a public statement saying he reported to the police on Thursday, saying he had received a message that unless he advised in favour of a pardon for Yorgen Fenech, the magnate would implicate him over two telephone conversations.
The protest is being held in Valletta in Castille Square, outside the Office of the Prime Minister.
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Three men have been awaiting trial for setting the bomb that killed Caruana Galizia, but so far the authorities have failed to track down the person who hired them.
Mr Cardona was briefly questioned by police on Saturday.
Mr Mizzi resigned on Tuesday and Mr Cardona has "suspended himself" from his duties.
Speaking to the BBC, the editor-in-chief of the Times of Malta, Herman Grech, said the anger aimed at Mr Muscat was extraordinary, especially given his widespread support.
Leaked emails revealed in court appeared to show both Schembri and Mizzi stood to receive payments from a Dubai company called 17 Black, owned by Fenech.
In the separate hospital case, Judge Edwina Grima ordered a criminal investigation into Mr Mizzi, Mr Cardona and Finance Minister Edward Scicluna over the granting of a contract to Vitals Global Healthcare to run three state hospitals.
The suspected middleman, Melvin Theuma, was granted a presidential pardon on Monday in return for evidence that could be used in court to convict those suspected of ordering the killing.
Mr. Schembri has denied all accusations of a role in the journalist's murder. Since October, 2017, when Mr. Caruana Galizia was murdered in a vehicle bomb explosion, he and several of his closest associates and cabinet members have been bombarded with accusations of corruption, conflict of interest and stalling the delivery of justice in the case of the slain journalist, who had devoted her career to exposing wrongdoing at the highest levels of government.