It stated that Fenech was ready to supply information related to, among others, Schembri, Mizzi and Chris Cardona, who suspended himself from the post of economy minister earlier this week.
Both Mizzi and Cardona denied having been involved in the death of Caruana Galizia, who was killed by a auto bomb after the publication of the Panama Papers, where she worked, exposed global corruption.
On Thursday evening, as Muscat and his ministers met behind closed doors, police said Schembri - who was arrested on Tuesday - had been released.
Sources told AFP that Schembri had been called in for questioning by police after his name was mentioned by the main suspect in the case, business mogul Yorgen Fenech.
Police questioned Schembri, but later let him go.
His detention followed that of a middleman in the murder, Melvin Theuma, who on Tuesday was given immunity to expose those involved.
Local media reported that he had handed over audio recordings.
Muscat has been heavily criticised over the government's handling of the case, and on Tuesday vowed to resign if links were found between himself and the murder. "Whatever people can say, there is no impunity in this country". Schembri denied acting badly.
Lately, though, the investigation has appeared to gather momentum after police detained businessman Yorgen Fenech last week.
"Since this case is about persons very close to the prime minister, it should not be the prime minister or a member of his cabinet to give such advice", Fenech's lawyers said.
Fenech also alleged that Arnaud had a conflict of interest, having previously sought the chief of staff's help in finding a job for his wife.
Three men are awaiting trial for setting off the bomb that killed Ms Caruana Galizia, and police sources said the investigation into who ordered the killing had made significant advances in the past week.
Neither Fenech nor his lawyer have made any comments since his arrest.
Caruana Galizia had been a towering figure in the small Mediterranean nation, best known for her work at The Malta Independent and frequent reports digging into the Panama Papers, a massive trove of law firm records leaked in 2016. Mr Schembri denied wrongdoing.
Mr Muscat told police the bomb had been placed in Caruana Galizia's vehicle while it was parked outside the walled compound where she lived.
Caruana Galizia's son Matthew tweeted that Muscat "simply can not be trusted to not obstruct justice".
"I felt it was my duty to step down from minister for the government of Joseph Muscat, which we worked so hard to elect, to be able to do its full term in office", he told journalist after a meeting of the Labour Party's parliamentary group.
Dunja Mijatovic, human rights commissioner for the Council of Europe, said she was "seriously concerned by recent allegations of political interference in the investigation" and called on Mr Muscat to prevent the appearance of collusion.
During a debate in Parliament, the country's opposition leader, Adrian Delia, told lawmakers that Malta's government "has evidently been hijacked by a criminal organisation".