The French navy has located one of its submarines that disappeared more than 50 years ago with 52 crew on board.

La Minerve was discovered on the seabed in the Mediterranean off the port of Toulon.

“It’s a success, a relief and a technical feat,” Florence Parly, the defence minister, tweeted. “I am thinking of the families who have waited for so long for this moment.”

La Minerve was on a military exercise when it disappeared in January 1968. Repeated searches have failed to find the vessel until now.

Under pressure from relatives of crew members, a fresh search was launched at the beginning of this year using the latest hi-tech equipment to map and model tides and currents in the Mediterranean. Data from the time of the accident was also re-examined. This included seismic reports that suggested the submarine probably imploded as it dropped to the bottom of the sea.

Facebook Twitter Pinterest The crew of La Minerve in 1965. Photograph: STF/AFP/Getty Images

A senior French naval officer told Agence France-Presse the submarine was discovered by a boat belonging to the private US company Ocean Infinity. It announced it had found La Minerve at a depth of 2,370 metres, 27 miles (45km) from Toulon, which is home to a French naval base.

The cause of the accident that led to the submarine sinking in just four minutes has never been established. Families hope the wreckage will provide long-awaited answers.

The son of La Minerve’s commander, André Fauve, said it was a moment of “great emotion” for the families of the submariners who perished. “Many people told me they were supporting me during the search because they didn’t want me to feel alone but they didn’t believe it would be found,” Hervé Fauve told Le Monde.

François Meunier, whose brother Marc was a quartermaster on La Minerve, said: “It’s the end of a long wait and many questions.”

The submarine, which had reportedly broken into three pieces, was located by Ocean Infinity’s search ship the Seabed Constructor, which arrived off the French coast five days ago. Using underwater drones, it found the wreckage on Sunday, helped by the fact that La Minerve had sunk in an area of low sedimentation. The first three letters of the vessel’s name were clearly visible on one piece of wreckage.

Facebook Twitter Pinterest A photo taken in the second half of the 1960s showing La Minerve docked in Marseille. Photograph: STF/AFP/Getty Images

Initial reports suggested the submarine may have had rudder problems before sinking. It was engaged in an exercise with a military aircraft when it disappeared at about 7.55am. The alarm was raised when it failed to return to its base the following day. About 20 boats, helicopters, aircraft and even a diving vessel used by the French oceanographer Jacques Cousteau were involved but the search was fruitless.

In 2018, the Seabed Constructor found the San Juan submarine that sank in the Atlantic off the coast of Argentina.