UPDATE 1-Barracuda says Sourcefire rejects increased bid

(Adds dateline, details on revised offer)

NEW YORK, June 24 (Reuters) - The board of Sourcefire Inc (FIRE.O) has rejected an increased takeover offer from privately-held Barracuda Networks which values the software maker at around $203 million, Barracuda said on Tuesday.

Barracuda said in a statement the new offer of $8.25 a share, up 10 percent from its earlier bid, was conveyed to Sourcefire board on June 9, but has been once again rebuffed by the company's board.

Sourcefire's board rejected the initial $7.50 a share offer as inadequate.

Sourcefire shares closed at $7.64 on Tuesday.

Barracuda said that despite the refusal of its revised offer, it hopes to continue a dialogue with Sourcefire's board and reach mutually agreeable terms.

The new offer values Sourcefire at about $203 million, based on about 24.6 million shares outstanding, as of Feb 25. (Reporting by Euan Rocha; Editing by Lincoln Feast)