BOSTON (Bloomberg) — Bermuda-based Tyco International Ltd. threatened to take away the right of bondholders to approve its break-up plan after more than two-thirds of its debt investors refused to tender their securities because they say the offer is too low.Tyco may waive the "majority consent" covenant in its bond indentures, the company said in a press release on Friday. Tyco bondholder American International Group Inc. this week sued the owner of ADT security systems in an effort to block it from buying back $6.6 billion of debt as part of a plan to split into three companies.

Bondholders claim Tyco, which also makes health-care and electronics products, is offering about $95 million less than what they are entitled to under the indentures. Tyco has said it is paying market rates.

"If they can somehow get the bondholders to agree, the upside is enormous," said Adam Cohen, New York lawyer who advises hedge funds on the value of bond covenants. "What risk do you have? A couple of million in legal fees and angering some people? It's a cheap option."

Tyco said on Friday that holders of less than one third of its US debt, totalling $5.6 billion, agreed to the tender. It also said it was extending the offer, which expired at 5 p.m. on Thursday, by three days.

The company has claimed in statements that it doesn't need bondholders' permission to go through with the break-up because the plan doesn't affect "all or substantially all" of the assets backing the bonds. AIG, in its lawsuit, disagreed.

A federal court hearing is scheduled for 5 p.m. on May 14 in the Southern District of New York in Manhattan. Andrew Rosenberg, a lawyer at Paul, Weiss, Rifkind, Wharton & Garrison LLP that is representing AIG didn't immediately respond to telephone messages and e-mail requests for comment. Tyco spokesman, Paul Fitzhenry, declined to comment.

Tyco's tender is the latest to test bondholder resolve against offers that debt investors say are less than what they are entitled to under their lending agreements. Bondholders united in January to force Blackstone Group LP to pay almost $225 million more than face value for the bonds of Equity Office Properties Trust this year when it bought the company.

"It comes down to lawyers and a more aggressive campaign to scare bondholders," said Glenn Reynolds, chief executive officer of independent research firm CreditSights Inc. in New York in an e-mail.