Via satellite phone yesterday Mr Tipoki said the ship had been "on the run" but was "caught" by the waka about 10am.
"We came alongside the [Amazon Warrior] and via radio calls to the Captain conveyed they were to leave our waters immediately."
Te Ikaroa spokeswoman Tina Ngata also told the captain of the Amazon Warrior they were in breach of the United Nations Declaration on the Rights of Indigenous Peoples.
Te Matau a Maui general manager Wayne MacGiliviray - acting as spokesman for the group while they were out at sea - said he was told the captain had listened to the group's message, and gave a "professional" response.
This is not the first time the Amazon Warrior has been intercepted - in January Tipoki joined a Greenpeace flotilla to confront it.
And on March 3 another waka, Ngahiraka Mai Tawhiti, delivered a similar message on behalf of his peoples of Ikaroa Rawhiti.
When asked what difference this voyage would make, Mr MacGiliviray said it would build momentum for the message they wanted to send.
"The message is really clear that they need to stop their work, and that they're not welcome," he said.
This was supported by Hawke's Bay Regional Councillor Paul Bailey, who said it was important to keep these sorts of issues at the forefront of people's minds.
The waka is due back in Napier this morning.