The tiny Pacific nation of Nauru has congratulated itself on a "world record" Covid-19 vaccination drive which resulted in all its adult population receiving their first shot.

The remote island nation is one of the few places in the world to remain virus-free and has now also become one of the first to give at least one shot to all adults.

Authorities in Palau, another far-flung island nation in the Pacific, say they are on the verge of a similar feat, with 97 percent of adults receiving their first jabs.

The Nauru government said its four-week campaign exceeded expectations as vaccination centres stayed open for extended hours to ensure maximum access.

It said 7,392 people received the first dose, or 108 percent of the estimated adult population, with foreigners included in the figure.

The second shot is expected to be administered by mid-July.

"The National Coronavirus Taskforce is extremely pleased with this world record result and thanks everyone on Nauru for playing their part," the government said in a statement.

Nauru received AstraZeneca vaccine doses as part of the global Covax programme aimed at boosting immunisation in poorer nations.

Task force chairman Kieren Keke said Nauru was fortunate to have enough doses to cover its adult population but there was no room for complacency, with testing ongoing to ensure the island remained virus-free.

"With every arriving traveller, the risk of the coronavirus entering Nauru remains and recent events in PNG (Papua New Guinea), Fiji and India have shown how quickly the situation can change," he said.

In Palau, officials say they hope to have 80 percent of the entire population of 18,000 fully vaccinated by the end of the month, a proportion they believe is large enough to give the nation herd immunity.

Palau recently opened up a travel bubble with Taiwan, hailing it as a "ray of light" that would not only help its devastated tourism sector but also show the world is slowly emerging from the pandemic.