TOKYO, Sept 3 (Reuters) - U.S. buyout fund Bain Capital

said on Tuesday it made a counter-offer to buy Japanese software

developer Fuji Soft, estimated at about 600 billion yen

($4.1 billion) that would exceed a rival offer from equity fund

KKR.

Bain said in a statement it made an offer at about 5% over

the 8,800 yen per share tender offer made last month by KKR. The

stock closed at 8,970 yen on Tuesday.

Fuji Soft's management has been at odds with some of its

major shareholders, including Singapore-based fund 3D Investment

Partners.

Fuji Soft said in a separate release that it received a

non-binding offer from Bain in July, and that its board would

consider any legally binding proposal.

In March, 3D, Fuji Soft's top shareholder with a stake of

some 21%, proposed that the company appoint an outside auditor

to ensure it fairly review multiple takeover proposals it had

received from global private equity firms.

($1 = 146.3900 yen)