New Delhi, Feb. 24 -- Paramount Skydance Corp. raised its offer to buy Warner Bros. Discovery Inc., extending the long-running battle for one of Hollywood's iconic studios, according to people familiar with the matter.

The new, unspecified bid improves on the $30-a-share, all-cash proposal that Paramount took directly to Warner Bros. shareholders on Dec. 8 and addresses some of the company's concerns with previous Paramount bids, according to the people, who asked to not be identified because the details aren't public. Those concerns include greater certainty of Paramount financing.

The media giant agreed in December to sell its film and TV studios and HBO business to Netflix Inc. for $27.75 a share. That deal involves a spinoff of Warn...