Health insurers are offering months of free cover to attract members in a promotions frenzy that has triggered a federal government probe into whether funds are breaching rules capping the discounts they can offer.

Dozens of funds, including Medibank Private, Bupa and Nib, are offering free cover for up to three months, potentially saving new members thousands of dollars if they sign up. Many are waiving wait times for dental and optical cover, and throwing in incentives including frequent flyer points or a chance to win a car as they ramp up promotions to lure new customers.