FORT-DE-FRANCE, France - France's government on Tuesday warned of an "extremely serious" COVID-19 crisis in the country's overseas territories, especially in the Caribbean, saying that infection rates had climbed to levels unprecedented on the mainland.

Martinique tightened a lockdown and told tourists to leave while similar measures were also expected on the nearby French overseas territory of Guadeloupe, a huge blow to the Caribbean islands at the height of the summer season.

While well over half of people in mainland France have now received two vaccination doses, rates in its overseas territories, from the Caribbean to the Indian Ocean to the Pacific, have lagged well behind.

"The situation is extremely serious," French Overseas Territories Minister Sebastien Lecornu told AFP before heading on a crisis visit to the French Caribbean, where he was due to be joined by Health Minister Olivier Veran.

"There are infection rates that have never been seen not just in these territories but all of France," he said.

"The Delta variant is more contagious and is hitting a population that is not well-protected" by vaccinations, he added.

Authorities on Martinique late Monday announced that all non-essential shops would now be closed, as well as hotels and holiday rentals, adding that tourists should leave. Beaches would also be closed and people can only go within a one-kilometre (0.6-mile) radius of their homes.

There are now 1,200 cases per 100,000 inhabitants on Martinique, while only 22 percent of the population have received even a first vaccine dose.

"These rules are strict and they will be lifted as soon as the health situation allows it," the top official of Martinique, Stanislas Cazelles, told reporters in its main city of Fort-de-France.

- 'Infinitely sorry' -

Guadeloupe is under less rigid restrictions than Martinique, but Lecornu indicated that he would discuss the need to put the island into a fuller lockdown.

"We will need to apply braking measures, there is an urgency," he said, adding that the island now had 1,700 cases per 100,000 inhabitants.

Veran had earlier this week made a video plea on social media for medical workers in mainland France to show "national solidarity" and volunteer to help stretched medical teams on the islands. Some 240 volunteers are now due to leave on Tuesday.

In the Pacific territory of French Polynesia, authorities meanwhile announced a curfew from 9:00 pm to deal with rising cases.

Tensions have been raised after a wedding party at a restaurant was attended by hundreds of people -- including top local figures -- in defiance of existing rules and without wearing masks.

"We were not exemplary and I am infinitely sorry," said the territory's president Edouard Fritch, who was seen playing the guitar in images of the party that shocked many Polynesians. The mayor of the capital Papeete, Michel Buillard, was pictured providing the vocals.

The Indian Ocean island of Le Reunion also remains in partial lockdown, a measure which like in the Caribbean has prompted protests that led to scuffles with the security forces.

The British government initially linked more stringent quarantine restrictions on people entering the UK from France to the outbreak on La Reunion, a concept that baffled French ministers who pointed out the island is several thousand kilometres from Europe.

London has since dropped the additional restrictions.

France's overseas territories -- left under French rule even after the end of colonialism -- are integral parts of the country's territory and give Paris a valued strategic footprint across the planet.