At least five unidentified drones have flown over the Eiffel Tower, the US Embassy and other Paris landmarks overnight, authorities have said.

The first sighting was near the US embassy in the French capital just after midnight on Tuesday morning, prompting police to follow the unmanned aircraft which continued on towards the Invalides military museum.

Police lost sight of the drone but later in the night, four other pilotless aircraft were spotted at several landmarks including the Eiffel Tower, the Place de la Concorde and the Montparnasse tower, the tallest skyscraper in the city.

"It could be a co-ordinated action but we don't know for now," a police source told the AFP news agency.

"We did everything to try and catch the operators but they were not found," another source close to the case said.

Frqance has seen a series of mysterious drone overflights at nuclear plants, and more recently over the presidential palace, with the fresh sightings coming at a time of heightened security following last month's attacks in Paris that left 17 people dead.

Flights over nuclear plants

In October and November, about 20 of the unidentified aircraft flew over French nuclear plants and their operators were never found.

French authorities have said the drones currently present no threat, but the government is trying to find ways to counteract the devices.

Drones come in all shapes and sizes, and have a variety of uses, from widely reported military applications to surveillance, filmmaking, sports, disaster relief and scientific research.

The most basic unmanned aircraft are radio-controlled by someone nearby, but other more sophisticated models can be pre-programmed, and these are widely available for as little as $440.