Yesterday he said: "We need to know, is John Key effectively trying to replicate Prism in New Zealand by getting this organisation Palantir to set up here and start spying on all of our internet communications and everything digital that we do?"
In Parliament he questioned Mr Key on what contact New Zealand intelligence agencies had with Palantir but Mr Key said it was his long-standing practice not to discuss operational matters and contracts of those agencies.
The Prime Minister confirmed he had met Mr Thiel - who sometimes lives in New Zealand - a few times but said he had never discussed intelligence matters with him.
Mr Thiel, a billionaire Silicon Valley entrepreneur and former PayPal chief executive, was "extremely generous after the Christchurch earthquake", Mr Key said.
Dr Norman later tweeted: "When crony govt meets surveillance state - John Key appoints Peter Thiel's Palantir to spy on NZers".
That drew an angry response from Mr Drury who tweeted: "Don't be w***ers", and followed that up with "Hey Greens. Cheating NZ out of $200m on Mighty River Power now spinning this rubbish. Please put NZ ahead of yourselves."
He said the Greens were "ruining relationships and/by insinuating cronyism is vandalism. Politics in NZ is getting nasty. Lift the game."
State Owned Enterprises Minister Tony Ryall said Dr Norman suffered from paranoia and called him the Chicken Little of New Zealand politics. "Every time he talks about anything the sky's falling in ... it's all big business big politics, the right against the innocent little Greens."
Mr Thiel's Valar Ventures and Matrix Capital Management hold 7 per cent of Mr Drury's Xero software company. Mr Drury did not respond to the Herald's calls yesterday.
Palantir has been under scrutiny in the US since news of the NSA's Prism system broke last week but the company said its Prism product "is completely unrelated to any US government program of the same name".
Palantir's products, however, are used by US intelligence agencies to mine and find links between pieces of data held across their databases.
Meanwhile, Dr Norman says New Zealand should offer to take US Prism whistleblower Edward Snowden, who is believed to be in self-imposed exile in Hong Kong as a refugee.
"I'm saying Snowden should be protected. If New Zealand can protect him, then we should."
Mr Key said it was a ridiculous idea.