The prospecting started at 6.30am, Spanish media reported on Tuesday
The oil exploration vessel being used, the Rowan Renaissance, is carrying out the first deep water survey, 50 kilometres (30 miles) from the islands of Lanzarote and Fuerteventura, off the west coast of Africa.
Spain's Industry Ministry earlier this year authorised Repsol to look for hydrocarbons in the area by probing at three locations at depths ranging from three to seven kilometres.
The exploratory phase should last about four months and the company estimates its chances of finding oil in the region are of 17–19 percent, according to its website.
Locals and green groups oppose the oil exploration. Residents fear Repsol's explorations will harm local flora and fauna such as dolphins and disrupt the tourism industry that is vital to the area's economy.
They have tried to stop the prospecting going ahead.
A Greenpeace activist was hurt Saturday in a confrontation with the Spanish navy that intervened during fresh protests against the exploration project.
The propellor of a Greenpeace boat cut and broke a 23-year-old Italian woman's leg after she fell overboard during the dawn clash, according to Spanish authorities.
The Spanish defence ministry said the navy believed the activists were trying to board the oil exploration vessel Rowan Renaissance, and had moved in to halt three Greenpeace boats. However, the activists say they intended to carry out a "peaceful protest."
The clash with the Spanish navy vessels on Saturday, came just one day after rallies against the oil exploration were held across the Atlantic archipelago, whose beaches are a popular draw for foreign tourists from Britain, France and elsewhere.
The Canary Islands regional government called a referendum to allow residents to vote on it, but the national government in Madrid has blocked that in the courts.