However, seven Greenpeace activists boarded the ship early on Friday to protest against the planned drilling.
The protest was into its fourth day and the six remaining activists had spent 77 hours on top of the 53 metre drilling tower.
"This chapter has ended, but the story of the battle to save the Arctic has just begun," Lucy Lawless said in a statement before being arrested.
"Seven of us climbed up that drillship to stop Arctic drilling, but 133,000 of us came down."
Greenpeace said more than 133,000 people sent an email to Shell executives telling them to cancel their plans to drill in the Arctic, which they said caused Shell's email systems to overload repeatedly.
Greenpeace New Zealand this morning announced on Twitter and on their website that police had arrived on the scene.
"Hello, two car loads of very well equipped police have just arrived on the wharf," @GP_Viv, one of the activists aboard the ship, said on Twitter about 10.20am.
"The police have started climbing the ladder," she tweeted at 10.55am.
Police confirmed they have climbed the tower and are talking to the protestors - asking them to come down peacefully.
Lawless tweeted that she is "anticipating imminent arrest" and is cleaning up the campsite.
"Will be disappointed if we have to leave but will go peacefully."
Earlier this morning she told Radio New Zealand the group had enough supplies to last "a couple more days", but assumed she would be eventually arrested.
"I don't know what that's like (to be arrested) but I understand that is how these things go. So I expect that."
She told Newstalk ZB the group would leave peacefully if police turned up, and would not make them scale the 53 metre drilling tower the protesters were up, she said.
"We'd never make them do that, that's unsafe ... we wouldn't put them in that position.''
Earlier the group had vowed "Guantanamo" style tactics would not bring them down from a tower aboard a Shell ship bound for the Arctic.
The six had spent a "gruelling" night last night at Port Taranaki, according to Greenpeace NZ climate campaigner Steve Abel.
Bright lights and loud music through the night kept the group awake but they remained "resolute, determined to stay".
Lawless posted on Twitter last night: "Loud music over speakers about 1.30 AM. They starting to go Guantanamo on our ass?".
She tweeted this morning: "...I found last night pretty darn scary. Not for sissies".
Mr Abel described the music as "loud, sort-of hard rock", and said no one had taken responsibility for playing it.
Shell corporate communications manager Shona Geary said the lights were necessary for the ships crew to carry out routine work.
"It appears that last night the protesters disabled the light at the top of the drill tower. These lights are there for safety reasons. A spotlight was used instead to light up the mast to help ensure the group were safe during crane and other night time operations."
She also said no loud music was played, and the sound was "coming from an alarm clock".
In a video published on Greenpeace NZ's website this morning, Lawless described the night as "pretty dark, dark in your soul".
Mr Abel said it has been difficult for the protesters to see the global response to their actions first-hand, which might have an alienating effect on the group.
"When you're in the absolute thick of it, it can sometimes feel very lonely."
He said the group were determined to remain atop the ship's 53m drilling tower as long as they had food and water.
"It's not something that can go indefinitely but, at this stage, they're confident they've got enough to last them a while yet."
Greenpeace's website said more than 123,000 people had joined its campaign, sending emails to the CEO, director and vice-president of Shell.
"The principle of this thing is that an oil spill in the Arctic would be impossible to clean up and that's exactly why Shell shouldn't even begin", Mr Abel said.
In a press release, chairman of Shell New Zealand Rob Jager said he was disappointed in Greenpeace's unco-operative stance and was concerned about the welfare of the activists still onboard.
"It was good to see yesterday one of the protesters halt his unlawful occupation of the drilling rig and the matter resolve itself safely. We look forward to the remaining protesters taking similar prudent and respectful action.
"Actions like this jeopardise the safety of all involved and our offer of an open conversation still holds."
He added: "Shell has taken unprecedented steps to pursue safe, environmentally responsible exploration in shallow water off the coast of Alaska."
Shell's oil spill response plan for the voyage was approved by the United States Department of Interior's Bureau of Safety and Environmental Enforcement on February 17.
Mrs Geary said she could not comment on the costs that the delayed departure was incurring.
- APNZ
