"The advantage, of course, is the passport," said Steinberg, "because with the German passport it's a lot easier to travel."
Travelers with German passports do not require a visa to enter the United States. Officials now believe at least one team of German jihadists was dispatched to Europe over the summer, travelling on German passports.
Steinberg said that many of the German jihadis who train in Pakistan are killed, "but those who come back are a threat. "And they are a threat not only to Germany," added Steinberg, "but also to our allies and especially the U.S. because they are extremely anti-American."
Steinberg said the Germans were recruited from mosques in Berlin, Bonn and Hamburg, including the same mosque in Hamburg where Mohammed Atta and other 9/11 hijackers gathered. German authorities shut down the Taiba mosque in Hamburg, previously known as the al Quds mosque, in August.
"Young men were being turned into religious fanatics there," said Christoph Ahlhaus, secretary of the interior for the city of Hamburg at the time.
"Hamburg cannot become a cradle for Islamists capable of violence," said Ahlhaus.
Steinberg said it was "quite shocking" that the former al Quds mosque was still producing jihadis. "There is a certain amount of continuity in German jihadism,' said Steinberg.
US officials said the CIA has been in frequent touch with European counterterrorism officials since the threat emerged this summer.
The threat may help explain the increase in U.S. air strikes in the mountainous area along the Pakistani and Afghan border.
There have been at least 70 attacks this year alone, with new ones announced each day, as General David Petraeus explained in an interview with Martha Raddatz of ABC News.
"The sanctuaries and safe havens, again, there will have to be more done about them," said Gen. Petraeus. "There were will have to be more pressure on them, no question."
In a statement to ABC News, Director of National Intelligence James Clapper declined to discuss the threat.
"We are not going to comment on specific intelligence, as doing so threatens to undermine intelligence operations that are critical to protecting the U.S. and our allies," said Clapper. "As we have repeatedly said, we know al Qaeda wants to attack Europe and the United States. We continue to work closely with our European allies on the threat from international terrorism, including al Qaeda. Information is routinely shared between the U.S. and our key partners in order to disrupt terrorist plotting, identify and take action against potential operatives, and strengthen our defenses against potential threats."
The FBI declined to comment.