A search of France's entire rail network for bombs has failed to find any traces of an explosive device, the national rail company, SNCF, says.
The French authorities say they are taking the threat seriously
The search was ordered after the French authorities received letters from a group saying it had planted 10 bombs.
The group, known as AZF, said it would explode the 10 devices unless a ransom of $4m and 1m euros (£2.8m) was paid.
This is the group's second such threat - in December a bomb was discovered on a track in central France.
"We know nothing of this group but we are taking the threat seriously," Interior Minister Nicolas Sarkozy said.
SNCF said the network remained under heightened surveillance.
Ten thousand rail maintenance workers began searching the country's 32,000-km (19,800 miles) network on Wednesday.
"These people are specialists. If any of the ballast around the tracks has been moved, if there has been any digging, they will notice straight away," SNCF's Francois Remy told BBC News Online.
Justice Minister Dominique Perben vowed to identify and capture the mysterious group.
"Everyone has been mobilised," he said.
The French railways have reassured passengers that there is no cause for alarm, but the government has been criticised for keeping the threat secret.
It had urged the media not to report on the case, and only confirmed the group's alleged existence on Wednesday.
"It's not right that the French people weren't informed about this from the moment it was being taken seriously," Jean-Claude Delarue of the Federation of Transport Users passengers' group told BBC News Online.
The group sent its first blackmail letter to the government in December last year.
In it, AZF said it was "a secular brotherhood with ethical and political connotations", according to the AFP news agency.
The group denounced "politicians more interested in themselves than the state", a "reductive education system" and an "economy that has lost its way".
A later note directed the police to a sophisticated explosive device laid on a viaduct near Limoges in central France on 21 February.
Experts, who carried out a controlled explosion, said the bomb was powerful enough to break a track.
In February a bomb was discovered on a rail viaduct near Limoges
The BBC's Caroline Wyatt in Paris says the group appears to be named after a chemicals factory in southern France where an explosion in 2001 killed 30 people.
Investigators believe that the explosion at the AZF plant was accidental.
And despite the seriousness of the threat, our correspondent says the story has taken on certain elements of farce.
Police kept in touch with the group via the personal ads in a French newspaper - with the police codenamed Suzy, and the group using the alias My Big Wolf.
A planned rendezvous earlier this week failed after French police were unable to locate the site nominated for the ransom drop.