The details of their disappearance still remain unknown, particularly after German boxing promoter Arena announced last month that it had signed them to five-year contracts.
Castro said: "They will be transferred provisionally to a guest house and they will be given access to their families. The press will also be able to contact them if it so desires."
The Cuban leader said that later "they will be offered decent tasks in sports according to their knowledge and experience.
"Brazilian authorities can rest easy in the face of inevitable campaigns by adversaries. Cuba knows how to handle itself in these circumstances. I, for my part, will sleep well."
The two men were arrested on Thursday by Brazilian federal police for overstaying their visas.
They were picked up in the coastal resort city of Cabo Frio, near Rio de Janeiro, where the games were held and where authorities said they had been staying at the resort and had run up a large bar tab.
Rigondeaux, 25, had failed to attend the weigh-in for his bantamweight bout at the games against Mexico's Carlos Cuadras.
Lara, 24, had not shown for his welterweight bout against Ricardo Smith of Jamaica.
Both men were disqualified and their opponents advanced to the semifinals.
The boxers claimed they had been contacted by a German businessman and that they had given their uniforms and passports to him.
Police said the pair had declined representation from lawyers which had apparently been sent by the same businessman.
Since the 2004 Olympics, Cuban boxing has been beset by defections, with several champions now plying their trade professionally in the United States and Europe.
Rigondeaux won the Olympic gold medal in 2000 and 2004 and is also a world champion.
He became Cuba's top boxer after the retirement of Mario Kindelan in 2004 and was aiming for his third Pan American Games title.