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Migrants and their homes in Germany faced more than 3,500 attacks in 2016, a number that is "alarmingly high and cause for concern," a German official said on Monday, while adding that the crimes are being aggressively prosecuted and the numbers of such attacks are now falling.

Most of the attacks were crimes like vandalism to asylum-seeker homes - including far-right graffiti, threats and slander - but the report also included more serious attacks like arson, bodily harm and attempted murder.

The study was compiled by the Interior Ministry with information from Germany's 16 states in response to a question in Parliament by the Left party.

"There was a very wide spectrum of crimes ... everyone is to be condemned," said Interior Ministry spokesman Johannes Dimroth.

The attacks led to 560 people being injured, including 43 children. Overall, 2,343 suspects were identified and investigated, according to the new report.

Comparison figures for previous years have not been compiled but Dimroth said after 2016 the "trend is downward ... which gives us a little bit of hope."

The sharp rise in hate crimes came after Germany took in some 890,000 asylum seekers in 2015 at the height of Europe's refugee crisis. 

Chancellor Angela Merkel's decision to open the doors to those fleeing conflict and persecution deeply polarised the country and fuelled support for the rightwing populist Alternative for Germany (AfD) party.

Earlier this month, a German neo-Nazi was sentenced to eight years in jail for burning down a sports hall that was due to house refugees, causing damage worth three and a half million euros ($3.7 million).

In another case that shocked Germany, dozens of onlookers cheered and applauded as an asylum shelter was set alight in the eastern city of Bautzen last February.

People were heard shouting "Good, that's up in flames", while police described the crowd as showing "unashamed joy" at the blaze.

The challenges faced by Germany in integrating the flood of newcomers are expected to become a hot-button topic on the campaign trail as the country heads for a closely-fought general election in September.