Signs of a bidding war for liability start-up PRI were met with disdain by suitor Brit Insurance Holdings.
PRI said on Tuesday it had received a higher offer than the £156m offered by Brit.
Brit seemed to be gaining ground in a tense battle for control over the new insurer when it revealed shareholder support for its offer had risen to 58.9% from 52%.
PRI, which projects to achieve gross written premiums totalling about £100m by the end of the year, responded by claiming to have received a better offer, but stopped short of revealing the new bidder's identity.
The company said in a statement that the new offer "could provide better value for PRI shareholders and represent a more compelling strategic combination than that proposed by Brit".
Brit chief executive Neil Eckert said the PRI shareholders supporting his offer had indicated they would only be tempted to back a rival bid if it was 20% higher than the Brit offer.
"If they can find someone else who's willing to pay 20% more then good luck to them," he said.
He described the new bidder as "mysterious", noting that PRI had not disclosed its identity or the value of its bid, but played down suggestions of mounting animosity between the companies.
PRI said that the new bidder could be in a position to make an offer by 25 April.
The company advised its shareholders to sit tight and take no action in respect of Brit's offer.