In France, repair work on three high-speed lines hit by arson has been completed before the official opening of the Olympic Games.
Trains are running on the lines again without delays, the state railway company SNCF announced.
On the route between Paris and southwestern France, virtually all trains would run according to schedule again.
On the route to the north, where trains run between Cologne and Paris, three of the four scheduled trains ran without delay.
The eastern line from Paris to Strasbourg, Stuttgart and Frankfurt has been running regularly again since Saturday.
The arson attacks on the night of Thursday to Friday caused serious disruption to rail traffic just before the start of the Olympic Games, affecting hundreds of thousands of people.
It is not yet known who is behind the attacks.
According to the newspaper Le Parisien, the attacks may have been carried out by radical left-wing activists.
On Saturday evening, Le Parisien reported that an unusual confession letter had been sent to several French and international media outlets, referring to the far-left.
The perpetrators claimed responsibility for the arson and claimed they wanted to disrupt the Olympic Games.
Investigators are now investigating whether it was a sincere confession to a false claim.
“We have a number of findings that give us confidence that we will know quite quickly who is responsible,” Interior Minister Gérald Darmanin told broadcaster France 2 on Saturday.