Cuba's state-run television reported that Total had inked a deal to explore for oil with Cuban state oil monopoly CubaPetroleo (Cupet), without providing further detail.

"Total categorically denies it has signed an offshore exploration agreement with Cuba," a spokesman said.

A source with knowledge of the matter said Total's marketing and services branch, which handles oil products distribution such as lubricants and jet fuel, had signed an extension to an existing letter of intent for a bitumen joint venture with Cuba.

Total has no existing exploration activity in Cuba, and in 2014 only had limited marketing activities for the sale of speciality products there, according to its annual report.

A dozen foreign firms have explored in Cuba's deep waters over the years, sinking four wells but finding no oil.

Total has explored close to shore, drilling two wells in the early 1990s. They came up dry and Total left in 1995.

For over a decade, Cuba has asserted its Exclusive Economic Zone off the northwest coast holds more than 20 billion barrels of undiscovered crude.

Last week Cuba unveiled new data it said confirmed there were billions of barrels of oil beneath its Gulf of Mexico waters.

The U.S. Geological Survey has estimated the region holds 5 billion to 7 billion barrels.

Venezuelan state oil firm PDVSA [PDVSA.UL] and Russia's state-run Zarubezhneft still retain exploration rights, according to Roberto Suarez Sotolongo, Cupet's co-director.

Cuba hopes the discovery of oil offshore will free it from dependence on other countries, such as socialist ally Venezuela.

French President Hollande, who was travelling with French business executives, this week became the first serving Western European leader to visit Cuba since Spanish Prime Minister Felipe Gonzalez in 1986.

(Reporting by Marc Frank in Havana and Michel Rose in Paris; Editing by Daniel Trotta, Lisa Shumaker and Dale Hudson)