"What we're seeing in connection with the refugee crisis is a mobilisation on the street of right-wing extremists, but also of some left-wing extremists who oppose them," said Hans-Georg Maassen on Deutschlandfunk public radio.
He added that for the past few years his service had witnessed a "radicalisation" and "a greater willingness to use violence" by all extremist groups, including the far right, the anti-fascist far left and Islamists.
Maassen spoke as Germany expects up to one million migrants this year, and after protests against refugee homes and clashes with police again rocked several towns at the weekend, mostly in the former communist East Germany.
Police and soldiers guarded two buses carrying about 100 migrants Saturday night to a shelter in the town of Niederau, in the eastern Saxony state, after right-wing protesters had rallied at the site, a former supermarket, since Friday.
More than 1,000 people also demonstrated against refugees in several towns in the eastern state of Mecklenburg-Western Pomerania Friday, including in coastal Stralsund where three people were wounded in clashes with counter-protesters.
In the eastern city of Leipzig, the right-wing rally "Offensive for Germany", organised by a local anti-Islam activist with about 400 marchers, sparked a larger left-wing counter-protest that police said drew more than 1,000 activists.
In the ensuing street clashes, the rival groups hurled rocks and fireworks at each other.
In the western city of Bremen unknown persons attempted to set fire to a tent set to house refugees from October.
This year alone has seen 22 arson attacks against would-be or existing refugee shelters, said Maassen, whose service is called the Federal Office for the Protection of the Constitution.