Germany experienced a spike in political extremism and violence from both far-right and far-left radicals as well as Islamist extremist groups in 2015, according to a report prepared by the country's domestic intelligence agency.

"Extremist groups, whatever their orientation, are gaining ground in Germany," interior minister Thomas de Maiziere said. "Security forces observed not just a rise in membership but also an increase in violence and brutality."

Last year some 1,408 acts of violence perpetrated by the the far-right were recorded, compared to 990 the previous year – a 42% increase. The report from the Federal Office for the Protection of the Constitution also noted 75 arson attacks on refugee shelters in 2015 – a fivefold increase on 2014.

More than a million refugees arrived in Germany last year, with many fleeing violent conflict in Syria and Iraq. But the move to welcome people in such high numbers has led to changing attitudes and a rise in confrontations and vitriol.

"The intensity of right-wing extremist militancy started in early 2015 and increased steadily, from threats against politicians and journalists to arson attacks on refugee shelters and attempted killings," the report says.

"It is worrying that anti-immigration incitement is creeping into the heart of our society," de Maiziere noted.

But acts of violence were not exclusive to the far-right and there was a noticeable increase in far-left extremism. Some 1,608 acts of violent crime were recorded in 2015 compared to 995 the previous year – a 61.6% increase.

According to the report, most far-left violence was perpetrated against the police or far-right radicals. "Extremist circles — of all orientations — are popular in Germany," de Maiziere noted.

The report also cautioned against the threat of Islamic extremism and said there could be up to 10,000 extremists in the country. It said some war criminals and jihadists are likely to have entered the country as refugees arrived in Germany in their numbers, but also highlighted the threat of being radicalised in Germany itself.