* Tenders running 'significantly' below minimum

* New deadline is June 12

NEW YORK, May 29 (Reuters) - Six Flags SIXF.OB extended its May 28 deadline for its note tender after the bids it received were "substantially below" the minimum level it had set, the North American theme park operator said on Friday.

The new deadline for tender is June 12 at 5 p.m. EDT (2200 GMT). The company is targeting 95 percent acceptance of the offer, which translates to roughly $825 million.

"Six Flags is extending the minimum tender condition in order to provide additional time for holders to consider tendering and provide its board of directors with ample time to consider the company's alternatives," the company said in a release.

In mid-April, Six Flags offered to exchange certain notes for common shares as part of a restructuring plan that would cut debt and stave off a Chapter 11 filing. The offer expires June 25, but the minimum tender deadline was set earlier.

The development is not unusual and is part and parcel of the negotiation process, said CreditSights analyst Christopher Snow. "It really pays for some bondholders to hold out to get a better litmus test to see how other react."

Six Flags, which offers 800 rides at its 20 parks, has been burdened with a massive debt load and a looming cash payment in August.

The company said it did not anticipate adjusting the deadline beyond the new deadline. If the minimum conditions are not met by June 12, the exchange would likely expire and Six Flags would cancel the meeting with holders of its Preferred Income Equity Redeemable Shares, or PIERS.