"We're trying to establish what their intentions are.''
Greenpeace spokesman Steve Abel said police were trying to climb the derrick to get to the protesters.
"We'd be pretty concerned about that because it requires specialist knowledge and capabilities to climb so you wouldn't want your everyday police officer having to do that without proper equipment. It's industrial climbing.''
The protest has captured international media attention with organisations including MSNBC, The Nation and the Associated Press trying to get interviews with Lawless, whose television series Spartacus is currently airing in the United States.
"Her involvement is very significant. There are very few people with her amount of profile and number of fans who have taken this level of non-violent direct action so, yeah, it's a pretty exceptional, historical event,'' Mr Abel said.
Police area commander for New Plymouth Inspector Blair Telford said their role in these situations was to ensure any protest was lawful and owners and crew of the ship were allowed to go about their lawful business.
"The protesters are clearly breaking the law by trespassing on the ship and we are currently liaising with the Port of Taranaki and the Harbour Master to decide the most appropriate course of action. Public safety is paramount.''
Lawless, the star of Xena: Warrior Princess, is a long-time Greenpeace supporter.
"I'm here today acting on behalf of the planet and my children,'' she was quoted as saying in a Greenpeace statement.
"Deep sea oil drilling is bad enough, but venturing into the Arctic, one of the most magical places on the planet, is going too far.''
Mr Abel said Lawless had decided to take part in today's activity of her own volition.
"She really was very keen to partake in a non-violent protest activity such as this one.''
She had considered that the police could be involved and people could be arrested, he said.
"She's got a strong passion for ensuring the Arctic does not become the latest frontier for the oil industry.''
She has taken to Twitter from the platform.
"All safe up here but a squall coming in. Good spirits,'' she tweeted.
"Today I'm taking direct action with GreenpeaceNZ in peaceful protest against Shell's Arctic oil drilling.
"I'm on one of the oldest drill rigs on the planet and it's heading to the Arctic. Tell Shell to stop.''
The ship was built in 1966.
Shell said in a statement it was "disappointed'' that Greenpeace had chosen this method of protest.
"While we respect the right of individuals to express their point of view the priority should be the safety of Noble Discoverer's personnel and that of the protesters.
"Shell has undertaken unprecedented steps to pursue safe, environmentally responsible exploration in shallow water off the coast of Alaska. We recognise the industry licence to operate offshore is predicated on being able to operate in a safe, environmentally responsible manner.''
Shell's Alaska exploration plans were guided by extensive Arctic expertise and world-class capabilities, it said.
