The French national suspected of shooting three people dead in Brussels' Jewish Museum last month has refused extradition from France to Belgium, prosecutors and his lawyer have said.

Mehdi Nemmouche, 29, has been in police custody since his arrest on Friday in the southern city of Marseille.

Prosecutors said the repeat-offender has been held under anti-terror laws on suspicion of murder, attempted murder and possession of weapons in relation to the attack on 24 May.

Prosecutors said that during an audience before a court in Versailles outside Paris, Nemmouche expressed his refusal to be extradited when presented with a European arrest warrant.

Nemmouche's lawyer, Apolin Pepiezep, told iTele Television his client preferred to be judged in France.

The suspect has another court appearance on Thursday at which France can demand that he be extradited against his wishes.

Nemmouche spent five jail terms in France before spending most of 2013 fighting in Syria with Islamist rebels, prosecutors have said.