A second share offering in a Government-owned power company should be available in October.
Shares in Mighty River Power began trading on Friday and the Government plans to partially privatise two other companies, Meridian Energy and Genesis.
Speaking on TVNZ's Q+A programme, State-Owned Enterprises Minister Tony Ryall said the Government would release further details of the float in the Budget on Thursday.
Mr Ryall is not ruling out some shares in Air New Zealand being sold later this year.
He said the Government is keen to have more New Zealanders investing in the share market.