TOKYO (Reuters) - U.S. private equity firm Bain Capital said it may withdraw its tender offer proposal for Japanese IT firm Fuji Soft, after rival suitor KKR raised its offer above Bain's in a protracted bidding war.

Bain Capital "is carefully considering its future policy, including the option of withdrawing" the proposal, it said in a statement on Monday.

KKR last week raised its offer price to 9,850 yen ($64.88) per share from 9,451 yen per share, above Bain's most recent offer of 9,600 yen per share in December.

Fuji Soft shares ended down 0.2% at 9,960 yen on Monday. The Tokyo stock market is closed on Tuesday due to a public holiday.

KKR currently has a 33.97% stake in Fuji Soft following the first stage of a two-part bid in which two activist investors - 3D Investment Partners and Farallon Capital - agreed to tender their shares to KKR.

Bain, which is supported by Fuji Soft's founding family, has yet to launch a tender offer.

($1 = 151.8200 yen)