The test was performed at 11pm Paris time beneath Mururoa Atoll in French Polynesia, the Defense Ministry said. It said the blast was equal to about 60,000 tons of TNT.
"This test was necessary to guarantee in the future the security and reliability of our arms," the ministry said in a statement.
France has been roundly condemned by governments and environmental groups worldwide for breaking a 1992 moratorium on nuclear tests with a blast on 5 September beneath the atoll, about 1,200 kilometers (750 miles) south east of Tahiti.
A second, more powerful blast was set off 1 October beneath neighbouring Fangataufa Atoll. France says up to eight underground tests are needed before May to check its nuclear arsenal and develop computer testing that will render future detonations unnecessary.
President Jacques Chirac has promised to sign a global test ban treaty after this last series of tests, and said earlier this week that the series might be cut back to just four more tests.
But he has been harshly criticised by European neighbours, the governments of the South Pacific and the environmental group Greenpeace, which has led a series of dramatic sea protests against the test. The French Navy has seized at least five Greenpeace ships after they crossed into the 20km exclusion zones around the atolls.
The government has been on the defensive lately over persistent reports that years of underground nuclear testing has fractured the undersea test site with hundreds of cracks, destabilising the atoll and increasing the chances that radioactive material might leak into the sea.
But France has refused to bend in the face of fierce criticism, pointing out that the tests are conducted about 800 meters (half a mile) below ground.
Britain said the decision by Paris to carry out a third nuclear test was purely a French affair, maintaining its refusal to join worldwide condemnation of the South Pacific tests.
"Our reaction would be exactly as it has been all the way through this series, which is essentially that this is a matter for the French government," said a spokesman for the Prime Minister, John Major. "The important thing is the work that's going on towards a comprehensive test ban treaty."
CND last night denounced Britain's failure to condemn the testing programme.Reuse content