The Federal Office for Security said criminals had infected computers with software which allowed them to gather email addresses and account passwords.

The agency has not commented on what progress it has made in tracking down the hackers.

It has set up a website for people to check whether they have been victims.

The agency learnt that the online criminals had managed to infect millions of computers with a program that would enrol them on to a network from where data could be stolen.

It believes most of those targeted are in Germany as many of the email addresses end in .de which is the identifier for German web addresses.

The scale of the attack is the equivalent of almost a fifth of the German population being at risk.

The BBC's correspondent in Germany, Steve Evans, said that so many people were anxious to check if they were victims of this hack that they overwhelmed the official security website causing it to crash.