Polish Kajetan Poznanski, 27, has admitted to the murder of his Italian teacher, identified only as Catherine, whose charred, decapitated body was found in a bag earlier this month.
The head was found in a back bag.
Mr Poznanski was arrested by plain clothes policemen at Valletta City Gate earlier this month and he was later extradited to Poland.
Questioned at the prosecutor’s office in Krakow for nearly four hours, Mr Poznanski, who faces life imprisonment, refused to be represented by a lawyer.
He is being held in custody.