Fidelity Life Assurance says two of its major shareholders plan to reject a $118 million takeover offer.
Fund manager and insurer Tower is offering $82 a share, made up of $55 cash, and $27 worth of Tower shares.
But it needs the support from 90% of shareholders to succeed.
Fidelity chairman Ian Braddock said in a statement that Tower's offer is unhelpful and inappropriate.
Mr Braddock says the board is evaluating the offer at the moment, but he doesn't think its in shareholders best interests to provide confidential or sensitive information to a competitor.
He says the company's commitment to independent advice has been critical to its success, and it plans to stick with that approach.
He says two of Fidelity's shareholders, who together own 70% of the company, won't be accepting the offer, but others should hold off making a decision, until an appraisal report is prepared.