Passenger Maureen Kelly said there was not widespread panic on board but "there were a few anxious people".
"We didn't really know what was happening. It was a bit scary, really. They didn't really tell us what was going on, just to get the lifejackets on."
She was on the dolphin-watching trip with members of her family. Most people remained calm, she said, including children on the boat.
"The kids were alright. I don't think they realised how serious it was, or could have been."
Another passenger on the boat said the port side had started to sink as it took on water.
The left-front of the boat was close to water-level, he said. The crew advised everyone to head to the highest point - the rear-right - of the boat, until they were rescued.
Three Coastguard boats and a nearby yacht helped remove passengers from the boat, before the police boat arrived and collected everyone together and returned them to shore, he said.
Inspector Ian Booker of police northern communications said it was not known why the vessel had started taking on water.
"It didn't hit anything, as far as we know, but it was just taking on water, so the people were offloaded as a precaution."
Mr Booker said the vessel was an 18m power catamaran with a capacity of 60 people. However, the vessel was "nowhere near capacity" at the time of the incident.
Coastguard spokeswoman Georgie Smith said three Coastguard vessels had responded to the Dream Weaver's distress signal and assisted the vessel back to Gulf Harbour Marina, where it would be "fully assessed".
Four crew had remained on the Dream Weaver, she said.
"They've done a wonderful job, and obviously the passengers have experienced a different afternoon, but they've done a great job in pulling it all together in what is a difficult circumstance."
Maritime New Zealand, which is responsible for investigating incidents on charter vessels, has been advised of the incident.
The rescue was followed by an electrical fire on board the vessel.
Fire Service northern communications spokesman Jaron Phillips said firefighters were called to the vessel at the Gulf Harbour Marina about 3.15pm.
"The fire is out, but crews there confirmed that it suffered an electrical fire in the engine area."
The cause of the fire was unknown, but police said the Fire Service's call-out took place long after the passengers had been removed and when the vessel was safely moored.
The MV Dream Weaver website describes the vessel as a "state-of-the art, purpose-built luxury charter catamaran".
It said the double-decker vessel was available for harbour cruises, corporate functions, weddings, dolphin tours, and other social events.
"The layout of the vessel is designed to provide the maximum on-the-water viewing experience without compromising comfort and safety and is superbly equipped for company meetings, multimedia presentations, networking or private occasion entertaining," the website said.
Staff from the Dream Weaver did not immediately respond to a message requesting comment.
