TOKYO—After spending weeks to resolve a massive Internet security breach, Sony Corp. Chief Executive Howard Stringer said he can't guarantee the security of the company's videogame network or any other Web system in the "bad new world" of cybercrime.

Mr. Stringer's comments in a phone interview Tuesday, ahead of a New York roundtable discussion with reporters, come on the heels of a trying month for Sony. The company partially restored two of its online game systems and a streaming movie and music service over the weekend...