TOKYO (Reuters) - U.S. private equity firm Bain Capital said on Monday it will not launch a tender offer for Fuji Soft, formally ending a takeover battle with rival KKR for the Japanese IT company.

Bain had said last week it might withdraw its proposal for Fuji Soft, after KKR raised its offer above Bain's in a months-long bidding war.

Previously, Bain had been waging the takeover battle even with rejection from Fuji Soft's board, arguing the rejection harmed the interests of minority shareholders.

However, KKR raised its offer price earlier this month to 9,850 yen ($65) per share from 9,451 yen, above Bain's most recent offer of 9,600 yen made in December.

Bain Capital said it wishes "for the continued growth of the target company under the renewed governance led by the new shareholders", in a statement on its website on Monday.

The saga epitomised an increasingly competitive dealmaking environment in Japan, as global investment firms target Japanese companies that are seen as having underutilised assets or ineffective corporate governance.

Shares of Fuji Soft, the Yokohama-based software and systems developer valued at more than $4 billion, were traded at the KKR-offered price of 9,850 yen on Monday morning.

($1 = 151.6100 yen)

(Reporting by Kantaro Komiya; Editing by Chang-Ran Kim and Muralikumar Anantharaman)