Sony on Monday offered frustrated gamers free video games and movie rentals as its online entertainment networks resumed normal functions after nearly a month of disruptions and data breaches caused by hackers.

“Playstation Network is once again operational,” Sony’s US social media manager Jeff Rubenstein said in a blog posting.

He said that US users of the company’s Playstation Network and PSP handheld console could choose two free games from a list of five titles. Customers were also offered a selection of movie rentals and extended network subscriptions.

“We developed the program as an expression of our gratitude for your patience, support and continued loyalty during the service outage,” Mr. Rubinstein said.

The resumption of the company’s online entertainment functions had been announced in Tokyo on Saturday, but a scramble of users trying to reset passwords and re-access the system sparked a torrent of technical difficulties that forced Sony to delay access for millions of users around the world.

Mr. Rubenstein said the majority of Sony’s online services are now operating normally. These include PlayStation Network and Qriocity (the company’s music and video services), online game play and video rental for Playstation consoles and access to services such as Netflix.

Sony said that the reconfigured entertainment networks had come back online in the Americas, Europe, Australia, New Zealand and the Middle East and included enhanced security features. In Japan the government had reportedly delayed the resumption of the services as it waited for Sony to provide more details of its anti-hacking and financial information protection measures.

Sony was forced to shut down the services in April as it investigated one of the largest data breaches ever, which exposed the personal details of some 100 million network users and possibly millions of credit cards, prompting government investigations of Sony in Japan, the US, Germany and many other countries.