"The bottom line that I can barely struggle to keep two P3s [surveillance aircraft] flying ... I just don't see that we have any spare capability right now to engage in that kind of a mission."
He said if we did have the capacity, Cabinet would have to discuss the matter and that no official request had been put in.
"Everything else is hypothetical beyond that point," Mark said.
The Minister said he had not been given a heads-up about Australia's decision, but understood a decision was pending.
New Zealand has two Anzac -class frigates currently in operation, the HMNZS Te Kaha and the HMNZS Te Mana.
National Party foreign affairs spokesman Gerry Brownlee described the admission as embarrassing and said New Zealand needed to join the effort, one way or the other.
"This is simply not good enough. New Zealand's Defence Force can offer its partners a range of skills and assets in a multilateral effort such as this," he said.
"Just as oil and other goods destined for Australia moves through the Strait of Hormuz, so too does oil and goods destined for New Zealand."
He applauded Australia's effort, saying the clock was now ticking for New Zealand.
Australian Prime Minister Scott Morrison on Wednesday described risks to shipping as a threat to his country's interests.
"Fifteen to 16 per cent of crude oil and 25 to 30 per cent of refined oil destined for Australia transits through the Strait of Hormuz," he said.
Australia now joins the UK, Bahrain and the US in the patrol effort.
It will send a Royal Australian Air Force P-8A Poseidon surveillance plane to the region for a month and an Australian frigate for six months from next year.
Foreign Minister Winston Peters in July condemned the tanker seizures as an "inexcusable violation of international law".
"Iran's recent actions risk escalating a dangerous situation in the Gulf region," he said.
Iran seized the British-flagged Stena Impero and the Panama-flagged MT Riah weeks apart in July.
Iranian armed guards also reportedly boarded the Mesdar, which is Liberian-flagged but British operated, but it was eventually allowed to continue its voyage, with all crew safe and well.
Iran has claimed it came to assistance of the MT Riah after it experienced mechanical problems.
Tensions in the region have escalated rapidly in recent months amid Iran's increasing frustration that it is not seeing the economic benefits of a 2015 agreement to limit its nuclear programme.
US President Donald Trump pulled the US out of the deal and re-imposed sanctions last year.
