A suspect accused of gunning down three Kurdish people in Paris told investigators of his "hatred of foreigners", the Paris prosecutor said on Sunday.

The 69-year-old man was arrested on Friday after two men and a woman were shot dead at a Kurdish cultural centre and nearby Kurdish cafe in the French capital's busy central 10th district. Police say the man was believed to be the only shooter.

The killings stunned a community preparing to commemorate the 10th anniversary of the unresolved murder of three activists, and prompted protests that led to clashes with police.

The suspect said during questioning that a burglary at his home in 2016 had triggered a "hatred of foreigners that became totally pathological", prosecutor Laure Beccuau said in a statement.

After being transferred to a psychiatric unit on Saturday, the suspect was discharged from hospital and his police custody resumed on Sunday afternoon, the prosecutor's office said in a later update, adding he would be presented to an investigating magistrate on Monday.

The office had already indicated on Saturday that a suspected racist motive had been added to initial accusations of murder and weapons offences.

During earlier questioning, the man described himself as depressive and having suicidal tendencies, recounting that he had planned to kill himself with a last bullet after his attack, the prosecutor said in the statement.

A search at the home of the suspect's parents, where he lived, did not find evidence of any link to extremist ideology, she said, adding that he had first sought potential victims in a suburb of the French capital but abandoned that plan.

The prosecutor had said previously that the suspect had been freed from detention recently while awaiting trial for a sabre attack on a migrant camp in Paris a year ago.

Kurdish representatives have called for Friday's shooting to be considered a terrorist attack.

Three other people were injured in the shooting. The prosecutor said two were still in hospital but their lives were not in danger.