The awarding of $444m in taxpayers’ money by the prime minister to the small Great Barrier Reef Foundation without consultation “stinks” and the money should be handed back, the Greens have demanded.

The party leader, Richard Di Natale, joined Labor in demanding the return of the huge sum given to the private foundation – which had just six full-time staff – and called for the whole process to be put to tender.

Speaking on ABC’s Radio National, Di Natale said the matter was a “massive scandal”.

“The prime minister and the energy minister have a private meeting with an individual ... this is an organisation made up of those at the big end of town ... and they give him half a billion dollars,” he told ABC’s Radio National.

“No tender process, no transparency, no examination of whether the organisation has the capacity to administer these funds.

“That money should be returned. There should be an open, transparent tender process and, if we had a national anti-corruption watchdog, this matter would be referred to it because it stinks.”

His comments came after the foundation’s managing director, Anna Marsden, said this year’s grant had come as a “complete surprise”.

Marsden defended the award, saying the foundation was the largest reef charity and the government wanted to encourage co-investment in the reef.

Asked about the fact that the foundation did not apply or complete a competitive tender for the grant, Marsden told ABC’s 7.30 it had come as a surprise.

She said 80 cents in every dollar raised was spent on reef projects, which would rise to 90 cents a dollar for the federal government grant.

Marsden identified climate change as the biggest threat to the reef, adding that efforts to protect it should “pull both levers: resilience and mitigation”. Australia “could probably be doing more” to meet its Paris targets and prevent climate change, she said.

The managing director disclosed that the foundation’s business partners included BHP, Google, Lendlease, Qantas and Rio Tinto, but said they had “no influence” on project selection or design.

Speaking again on Radio National on Wednesday she said: “We have a compelling track record … we have a phenomenal track record in delivery private and public partnership.

“Look what we have achieved with a fraction of this investment. Imagine what we can achieve with the scale up that has been promised.”

On Monday Turnbull defended the government’s “very thorough process” before the grant, explaining that both the expenditure review committee and cabinet had approved it before the money was offered.

The prime minister said the government had not put the grant out to a competitive tender because the foundation was an “outstanding” organisation and was “were clearly the best team to do it”.