Elevation Capital wanted NZX to adopt a new strategy to deliver value.
That included halving the executive team and trimming the board, and paring back NZX's operations.
Proposals included demerging its funds management business and selling down its dairy derivatives business into strategic joint ventures.
The fund manager wanted Bethunes Investments director John Fernandes to oversee that strategy, and for NZX's directors to repay their share of a recent trip to New York, where a memorandum of understanding was signed with Nasdaq.
The stock market operator said the demands from a shareholder with just 2.3 per cent of the company were unreasonable.
It didn't agree that the small differences outlined in Elevation Capital's alternative strategy, or Fernandes' appointment, would add value for shareholders.
NZX also defended the trip to New York, saying it was high value because the relationship with Nasdaq spans both technology and the market.
The stock market operator said it would prefer Elevation Capital didn't call a special meeting - which requires 5 per cent support - but that it will defend its position and update the progress to date if shareholders demand one.
Elevation said it was disappointed that its attempts to bargain in good faith were rebuffed. It will gauge how much support it has from other shareholders on what its next action should be, including calling a special meeting.
The fund manager has requested NZX's share register.
NZX shares rose 0.9 per cent to $1.09. Elevation reckons if the company adopts its initiatives, the separate funds management business and stock market operator could be worth between $1.62 and $1.89 within a couple of years.