Prime Minister John Key says there are measures the Government has up its sleeve to handle protesters who might try to delay the start of drilling by oil giant Anadarko off the coast of Raglan.
But he has refused to go into what those measures might be.
Protest vessels have so far prevented Anadarko drilling ship the Noble Bob Douglas from breaking ground below the West Coast of the North Island.
Work still hasn't begun at the site, 110 nautical miles west of Raglan, where Anadarko spokesman Alan Seay last week expected drilling to commence on either Thursday or Friday.
One GreenPeace vessel - the Vega - has remained inside the 500 metre exclusion zone, but Anadarko has said it would begin drilling today.
Anadarko's licence began on November 15 and ends on February 14 and it is an offence for any vessel to get within 500 metres of the drillship.
On RadioLive this morning, Key refused to say whether or not the military would by called in to push the protest boat back outside the exclusion zone.
Key denied there was a large number of people in New Zealand worried about the safety of deep-sea drilling.
"There are people who are genuinely confused by the data and what they're told," he said.
This was after more than 3000 people showed up at coastlines across the North Island yesterday, to show their opposition to deep-sea drilling in New Zealand.
"You can't say there's no risk," Key said.
"But I think that risk is extremely remote.
"Technology has changed a lot, we have higher standards in New Zealand. I've seen what it would actually take for there to be a major problem, and there's an awful lot of things that would have to go wrong at the same time."
Support for the Vega, and the flotilla, has grown in recent weeks, with around 700 people turning out for a Banners on the beach protest at Raglan on Saturday, one of many run on the West coast of the North Island.
Kawhia tribe Ngati Hikairo attended the Raglan protest and another was held at Aotea Harbour.
More than 1000 people attended the deep sea oil protest at Auckland's Piha Beach, 400 at Muriwai Beach and 500 at Bethells Beach as the land-based demonstrators threw their support behind the protest flotilla.
Raglan Maori are also among those opposed to Anadarko's presence.
Tainui hapu environmental spokeswoman Angeline Greensill said they were considering legal action after the arrival of the gargantuan drillship on Tuesday.
The hapu has threatened to issue a trespass notice on the oil drilling company, which it says is drilling in Tainui's customary fishing waters.
"They are actually within our customary fishing area of the whole west coast, so we're just contemplating going out ourselves. They need to be served notice that they are trespassing on our rohe moana (ocean boundary)."
Greensill, a former Mana Party candidate, said discussions were under way between west coast Maori on how best to to protect their traditional food source.
She complained Raglan Maori were not consulted before the Government issued Anadarko a licence to prospect for oil in 1500 metres of water.