The company had said earlier it was aiming to restore all services by the end of May.
Also Read: Sony to move PlayStation Network to new data centre
A spokesman for Sony Computer Entertainment, the company's games unit, said the delay in Japan was due to the need to comply with government instructions on information security, but he declined to specify reasons for the delay in other parts of Asia.
About 90 per cent of the network's users are in North America and Europe.
PlayStation Network users in Japan have already had online play services restored but do not yet have access to other services, such as the PlayStation Store, where they can buy games.
Sony said in a statement it would announce details for Japan, Hong Kong and South Korea as they became available.
The Japanese electronics and entertainment company also said last week its officials will testify before US lawmakers at a hearing on data security in Washington on June 2 about what is thought to be the biggest ever Internet security breach.