Joseph Muscat has announced he plans to step down as Malta’s prime minister, saying on state TV he would ask his ruling Labour party to start a process to choose a new leader on 12 January next year.

He made the announcement on Sunday night after calls for his resignation had grown over the 2017 car bomb killing of anti-corruption journalist Daphne Caruana Galizia. On Saturday, a prominent businessman with alleged ties to government ministers and senior officials was charged over the case.

“I will write to the president of the Labour party so that the process for a new leader is set for 12 January 2020. On that day I will resign as leader of the Labour party. In the days after I will resign as prime minister,” Muscat said.

“Our country thus will start a short process of approximately a month for the Labour party to choose a new leader and a new prime minister.”

Thousands of people took part in an anti-government march earlier on Sunday in Valetta, the capital of the tiny Mediterranean archipelago nation, marching from parliament to the central court house in an event organised by the activist group Repubblika, among others, and led by members of the Caruana Galizia family.

Earlier, lawmakers from Labour had insisted they would stand by Muscat.

Yorgen Fenech, 38, was taken to a Valletta court late on Saturday and charged with complicity in the murder. He pleaded not guilty to that and other charges.

Joseph Muscat, Malta’s prime minister, has said he will be stepping down. Photograph: Yara Nardi/Reuters

The government had earlier turned down Fenech’s request for immunity from prosecution in return for revealing information about the murder plot and about alleged corruption involving Muscat’s former chief of staff Keith Schembri and the former tourism minister Konrad Mizzi, among others, court filings showed.

Schembri and Mizzi resigned on Tuesday. Schembri was interrogated for two days by police before being released without charge. He has denied any wrongdoing. Mizzi denied any business links with Fenech and any wrongdoing.

Before Muscat’s announcement, the Labour party’s parliamentary group met for four hours on Sunday at Girgenti Palace, the prime minister’s official countryside residence, saying afterward that lawmakers gave “unanimous support to all decisions which the prime minister will be taking”.

On Saturday, Caruana Galizia’s family called for Muscat, 45, to quit. The journalist had reported that Schembri and Mizzi set up secret companies in Panama. She also reported how another company, 17 Black, was meant to be a vehicle to deposit funds into those companies.

An investigation by Reuters and the Times of Malta showed Fenech as having been the owner of 17 Black.

Mizzi denied any business ties to Fenech or knowledge of 17 Black or any criminal activity.

Schembri has always denied any wrongdoing. Speaking on Saturday for the first time since his arrest, he denied being the author of a typewritten letter that Fenech told police he received anonymously after his arrest. Fenech said the letter told him to pin the blame for the murder on another government minister.

“I immediately denied that the letter came from me when the police were interrogating me and I stand by that completely,” he told the Times of Malta.