TOKYO (Reuters) - U.S. buyout fund Bain Capital made a binding offer to buy Fuji Soft for 9,450 yen a share in a deal that values the Japanese software developer at $4 billion and outbids rival KKR by about 7%.

Bain said in a statement on Friday it planned to launch the offer towards the end of October provided it can get Fuji Soft's backing.

Bain and KKR have been engaged in a rare showdown to take over Fuji Soft, which has been at odds with some of its major shareholders.

KKR last month brought forward the start of its tender offer by about a week at the unchanged price of 8,800 yen, and said it would conduct the tender offer in two stages.

Fuji Soft has since said its board had decided to recommend shareholders to tender shares to KKR's first tender offer.

Shares in Fuji Soft closed at 9,000 yen on Friday.

($1 = 149.1200 yen)