According to local reports, it is likely Muscat's move indicates a "plea deal" is to be negotiated. Elaine Mercieca, of Malta's Attorney General's office, said the suspect's lawyer had filed a "joint application" along with the Attorney General, to allow private submissions to the court regarding punishment.
Only lawyers and the Caruana Galizia family will be allowed to hear these points.
This development is a significant change from how the trial and case had been progressing.
Muscat's co-defendants, brothers George and Alfred Degiorgio, have both launched challenges to the legality of the case brought against them.
They are both pleading not guilty.
In a dramatic twist outside the court, police revealed they arrested three more people while the court proceedings were under way.
Jamie Vella and a second pair of brothers, Robert and Adrian Agius, were arrested on suspicion of providing the bomb that killed Caruana Galizia.