Paparazzi were kept at bay as the couple arrived in Egypt

Holding hands with Ms Bruni, the French president waved at onlookers as they arrived at their luxury hotel.

But security is tight with plainclothes guards deployed in the town and two journalists were briefly detained on Monday night after filming the hotel.

Mr Sarkozy, 52, divorced his wife of 11 years, Cecilia, in October.

He was first pictured in the French media with Ms Bruni, 39, in mid-December during a visit to Disneyland Paris.

Private jet

The former model, who has been previously linked to men including Mick Jagger, Donald Trump and Eric Clapton, began a career as a singer after quitting the world of fashion.

Since leaving fashion, Bruni has launched a successful music career

The couple travelled to Egypt in an entourage reportedly including friends and relatives. They arrived on a private jet, courtesy of Mr Sarkozy's friend, the French billionaire Vincent Bollore.

To avoid the photographers' lenses, the pair boarded in a private aircraft hangar in France.

On their touchdown in Luxor, heavy security prevented the media approaching and an official photograph was released by local authorities.

It was reported that the couple were to visit archaeological sights around Luxor, which is on the banks of the Nile, on Christmas Day.

They were then to travel to another resort, Sharm el-Sheikh, on Thursday, French media say, although French authorities have refused to confirm the reports, saying it is a private matter.

Mr Sarkozy is then due to make a formal state visit to Egyptian President Hosni Mubarak in Cairo before flying back to France to see in the New Year.