The move came after "very strong interest during the first 24 hours of the bookbuild" with institutional investors such as investment funds, the government said.

As reported by The Australian Financial Review on Wednesday, investors flocked to the first day of the Medibank Private share auction for institutions, as fear of missing out pushed some fund managers to bid as high as $2.25 a share – more than 12 per cent higher than the initial suggested price range.

"The book is many multiple times covered at the top of the initial indicative price range," Medibank's advisers said in a message to investors on Wednesday. "Demand is currently represented from over 300 investors and is split approximately 50/50 domestic and international.

"At $2.10, the book is currently covered multiple times with high quality demand."

The revised price range means retail investors are almost assured a paper profit when Medibank starts trading next Tuesday November 25. The government has said that regardless of the final offer price retail investors will not pay more than $2.

At the upper end of the new price range, $2.30, retail stakes would open 15 per cent higher.

The share auction for institutions will run until midday on Thursday. The government will not announce the final price until Medibank's trading debut on Tuesday.

Strong demand for the float means the insurer is on track to eclipse the $4.6 billion privatisation of rail freight business QR National in 2010 as the biggest government asset sale since the $14 billion partial listing of Telstra in 1997.