This story (originally published on 8 March) has been updated to clarify the $68 million figure is an annual sum.
Government science agency Callaghan Innovation has started consultation on changes it says will cut costs.
The organisation held a meeting with staff this morning.
In a statement to RNZ, chief executive Stefan Korn said it had asked staff for feedback "on a proposed board directive to refocus the organisation on its core functions".
"We are proposing to refocus on our core functions to help relieve cost pressures," he said.
"While we are not consulting on a restructure at this time, a shift in strategy like this inevitably means uncertainty for many of our people."
Callaghan Innovation was established in 2013 and employs 430 people.
Prior to today's meeting Public Service Association assistant secretary Fleur Fitzsimons told RNZ Callaghan staff were feeling anxious about the organisation's plans.
"We're really worried about what's happening in Callaghan," she said.
"We know that they conduct new research including medical technology, medical devices as well as in physics and engineering that's not done anywhere else in New Zealand. So we really don't want to see cuts there or any cuts across the science sector in New Zealand. New Zealand really can't afford to spend less on science in this environment," she said.
She said the union's members were worried about funding problems for other government research organisations, including the seven crown research institutes.
That fear was driven by uncertainty about the future of science funding under the new government, she said.
Callaghan, crown research institutes and universities are facing the loss of about $68 million annually in research funding when the National Science Challenges end in the middle of the year.
The challenges programme had a 10-year life-span, but scientists had expected they would be replaced by a similar scheme before they expired.
They were also ruing the government's cancellation of its predecessor's plan to invest $450m in science infrastructure in Wellington.
"We're really concerned about the science sector in New Zealand. There are dark days ahead for science. We don't know what will replace the science challenges, we've lost the capital injection into Wellington through the scrapping of the Science City," Fitzsimons said.
She said it was also unclear how the government's push for savings of between 6.5 and 7.5 percent across the public service might affect science funding.