More huge waves are forecast for the Cook Islands, even as a clean-up is underway for damaged infrastructure and buildings in parts of the Cook Islands, American Samoa and French Polynesia.

This coastal restaurant at Aroa Beach on Rarotonga's ring road was badly damaged in the storm. Photo: Supplied/ Red Cross

Huge waves that struck the Cook Islands over the weekend are expected to hit Rarotonga and the Pa Enua (outer islands) again in the coming days.

Cook Islands emergency management director John Strickland told RNZ that nationwide alert notices would be issued to warn of another swell lined up to strike southern parts of Rarotonga on Tuesday (Cook Islands time).

Strickland said the clean-up operation was well underway on Rarotonga, with roads being cleared first, so that further damage could be assessed.

Roads, houses and businesses hit, as tourists returned to the Cook Islands

Late last week and into the weekend Rarotonga and some parts of the Pa Enua reported record waves and flooding that damaged homes and businesses, during a week when record visitor numbers had been expected.

Muri Beach Club resort manager Liana Scott said the waves were as high as during a cyclone.

King tides had been forecast to coincide with the storm, but even then the height of the waves and the distance the swell came ashore was a surprise.

"[On] the more eastern side of the island they had water go through rooms... sand dumping, removal of large boulders to the other side of the road - so it was quite surreal.

A government survey of the damage was circulated quickly, and one property reported $1 million worth of damage, including to guest rooms, Scott said.

"Where you were on the southern and eastern side of Rarotonga determined the extent of the damage," she said.

There had been heavy erosion in some places, with lots of debris left swirling in Muri lagoon.

"You can imagine ... this is quite a blow for tourism properties that are just coming into the middle of high season. It was quite difficult reassigning rooms for those guests, given the island is quite full at present."

King tides swamp homes in American Samoa

The state of emergency remained in place on Monday for American Samoa after huge sea swells flooded coastal areas of the islands of Tutuila and Aunu'u.

On Aunu'u, homes were swamped by king tides on both Thursday and Friday.

American Samoa's emergency operations centre said a channel between Au'asi and Aunu'u had been reopened after it was closed during the storm. Food for three days, as well as 40 cases of water was delivered to Aunu'u.

Some families had left their homes and moved further inland, and building that housed American Samoa Power Authority generators was partly washed away, with fuel drums washed out to sea.

American Samoa director of homeland security Samana Semo Ve'ave'a said preliminary damage assessments had begun and were continuing through Monday.

No injuries were reported, but coastal homes had been flooded and building materials to repair the Aunu'u seawall were washed away.

Roads and sea walls on the eastern side of Tutuila were extensively damage and the cost of the repairs would be significant, he said.

French Polynesia declares a natural disaster

A state of natural disaster was declared in French Polynesia after widespread destruction was caused by the unusually high swells.

Port structures and roads were damaged in the Marquesas, the Tuamotus and the Austral Islands.

Assessments of the damage continued, with the costs estimated to run into the millions.

Funds to help cover the repairs have been released by the government, after an extraordinary meeting was called.

Vice-president Jean-Christophe Bouissou said a first tranche of credits was expected to be released on Tuesday (NZ time).