The boat that arrived in Geraldton today with dozens on board. Credit:Ros Silcock

Inspector Dominic Wood said police had identified a refugee boat that arrived in Geraldton on Tuesday under its own steam.

"I suppose it would've been a surprise," he said.

"I don't recall any getting this far down [the coast] in recent times."

Inspector Wood said the boat had been met by customs and police officers in order to manage their security and safety.

It is understood that the boat was noticed drifting in the ocean near the foreshore just after 12pm.

Photographs of the boat on social media showed that children were on board the vessel.

A witness said the boat was seen drifting not far off the beach, close enough to see that it was overloaded with people.

They said it looked "rickety" and like no boats usually seen in the area.

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The witness said fisheries officers took a boat out to the ship and towed it away about 1pm.

Geraldton Guardian editor Alex McKinnon told Radio 6PR that there were 72 Sri Lankan people on board.

He said they had been at sea for 44 days and it was understood that they were headed for New Zealand.

"People are shocked, they are just standing on the foreshore," Mr McKinnon said.

He said their boat had the words "help us get to New Zealand," painted on it.

West Australian Premier Colin Barnett said he was alarmed that an asylum seeker boat could sail undetected into the Port of Geraldton.

"The State Government is working cooperatively with the Commonwealth on this issue and will ensure people's welfare is being looked after," he said.

"Nevertheless, this is a serious, unprecedented and unacceptable breach of Australia's border security.

"That a boat, laden with people, can sail into a busy regional port in broad daylight is shocking."

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It is highly out of the ordinary for an asylum seeker boat to travel this far south, with most asylum seeker boats arriving off the coast of Western Australia, near Christmas Island, thousands of kilometres north.

Geraldton is approximately 400 kilometres north of Perth.