A record 18,000 people have turned out for an anti-immigrant rally by a right-wing populist movement in eastern German city of Desden, prompting thousands to join counter-demonstrations in several cities.

The movement that began with just a few hundred in October against percieved "Islamisation of Europe" drew huge crowds on Monday despite calls by Chancellor Angela Merkel to snub such street protests.

Alarmed at the rising xenophobia, an estimated 30,000 people rallied against the "Patriotic Europeans Against the Islamisation of the Occident", or PEGIDA group across several cities.

Several thousand anti-PEGIDA protestors turned out in Cologne, some carrying placards stating "foreigner hatred is inhuman" or "shame for our country" while one held by supporters of the group read "think of your children".

Cologne's landmark Gothic cathedral dimmed its outdoor lights in a stand against the anti-Islam group.

In Berlin, more than 5,000 people rallied against PEGIDA. Justice Minister Heiko Maas joined the anti-PEGIDA protest, while the foreign ministry tweeted "there is no room for xenophobic agitation" in Germany.

A counter-demonstration in Dresden drew some 3,000, police said.

Anti-PEGIDA demonstrations were also held in the cities of Stuttgart, Muenster and Hamburg, the dpa news agency reported.

Over the last three months, crowds at PEGIDA's demonstrations in Dresden, Saxony, a region that has few immigrants or Muslims, have swelled from a few hundred to 17,500 just before Christmas.

PEGIDA calls itself a grassroots movement and according to its manifesto, aims to protect "Judeo-Christian" values.

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

The country has seen a significant rise in far-right extremism and attacks targeting foreigners, in Saxony, the number of anti-foreigner crimes reached 179, up from 152 the previous year and the highest level in over a decade.

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

PEGIDA has broadened its appeal by distancing itself from the far right, saying in its position paper posted on Facebook that it is against "preachers of hate, regardless of what religion" and "radicalism, regardless of whether religiously or politically motivated".

"PEGIDA is for resistance against an anti-woman political ideology that emphasises violence, but not against integrated Muslims living here," the group said.

It has also banned neo-Nazi symbols and slogans at its rallies, though critics have noted the praise and support it has received from known neo-Nazi groups.