The Mighty River Power share offer is underway, but details of how many people have signed up to buy the shares are not being revealed.
The Government intends to sell 49% of the state-owned energy company - the first of three companies up for partial privatisation.
The opportunity to formally apply for shares in Mighty River began on Monday morning. About 440,000 people pre-registered their interest and have three weeks to make a purchase.
However, there will be no updates on progress. An official in the Finance Minister office said securities law prohibits release of that information until the process is finished.
Mighty River Power is due to be listed on the New Zealand Stock Exchange on 10 May.
State Owned Enterprises Minister Tony Ryall said potential investors could go online from 8am and signal how much they want to spend.
The prospectus states that the price per share is likely to be between $2.35 and $2.80.
Eligible New Zealand investors will get one bonus share for every 25 shares they hold after two years, with a limit of 200 bonus shares.
The prospectus lists several potential dangers for investors, including political and regulatory risks.