In its monthly statement, the fund blamed its performance drop on falling global equity markets.
But a spokeswoman said the fund had since recovered some of the decrease.
For the financial year to May 31, the fund was down 1.12 per cent, meaning the June performance was likely to be around 1 per cent growth.
The spokeswoman said the June figures would not be published until August when the super fund released its annual report.
The fund, which had its contributions from the Government put on hold in 2009, has had an average annual return of 6.83 per cent since it was launched.
Its largest New Zealand investment is in Auckland Airport, while its biggest international investment is in a company called Transurban Group - an Australian-listed firm which specialises in owning and operating toll roads.
The super fund is also in the process of recruiting a New Zealand equities manager and several analysts to enable it to manage some of its money in-house.