German police have noted a significant rise in far-right extremism and attacks targeting foreigners, a news report said on Sunday, amid a growing debate about a new Islamophobic movement.

"We're seeing a significant nationwide increase in xenophobic offences," Federal Criminal Police Office chief Holger Muench told an interior ministers conference last week, the newspaper Welt am Sonntag reported, citing participants.

The trend is seen as a backlash against a sharp increase in refugees arriving in Germany, Europe's biggest economy and a top destination for asylum seekers and other migrants.

In the latest attack, three buildings reserved to house asylum seekers were set ablaze in the southern town of Vorra last Thursday, with Nazi swastikas and racist slogans scrawled on the walls.

Germany's domestic security agency estimates there are almost 22,000 far-right extremists in the country, more than a quarter of them neo-Nazis.

In the eastern state of Saxony, the number of anti-foreigner crimes has reached 179, up from 152 the previous year and the highest level in over a decade, the newspaper reported.

The state capital of Dresden has seen a rise in anti-Islam "Monday marches" under the slogan PEGIDA, "Patriotic Europeans Against the Islamisation of the Occident", which drew over 10,000 people last Monday.

Neo-Nazi links

The marches have been dominated by disenchanted citizens with a host of grievances, many waving German flags and chanting nationalistic slogans.

News magazine Spiegel, however reported that three PEGIDA organisers have criminal records and that the group has drawn support from the neo-Nazi and far-right football hooligan movements.

A poll for Spiegel by the TNS institute, found a majority of Germans were at least open to some of the views voiced by PEGIDA and the right-wing party - Alternative for Germany (AfD), which has voiced sympathy for the demonstrators.

Over a third, 34 percent, believed Germany was undergoing a process of "Islamisation", while 65 percent said the chancellor's right-left coalition was not taking current record levels of immigration and asylum seekers seriously enough.

Germany has an estimated 4 million Muslims, in a total population of nearly 81 million.

Chancellor Angela Merkel's spokeswoman on Friday condemned PEGIDA and its smaller clones in half a dozen German cities, saying: "There is no place in Germany for Islamophobia or anti-Semitism, hatred of foreigners or racism."

Merkel argues that Germany, whose population is ageing and shrinking, needs immigrant workers to avoid a chronic shortage of skilled labour.