Around 18,000 people have taken part in an anti-Islam rally in the German city of Dresden despite a plea by Chancellor Angela Merkel to reject the growing protests, which she has branded racist.

While the demonstration was the biggest so far, similar far-right rallies held in other German cities have been met by much bigger counter-protests.

Lights around the country were switched off in protest at the anti-immigrant demonstrations - monuments in Dresden were thrown into darkness along with Cologne Cathedral and Berlin's Brandenburg Gate.

The rapidly expanding grassroots movement Patriotic Europeans Against the Islamisation of the West (PEGIDA) has unsettled the country's political establishment in recent months with its weekly rallies in Dresden.

The protests have continued to grow from an initial few hundred people in October.

On Monday, protesters waved the German flag and brandished posters bearing slogans such as "Respect and tolerance for our people too" and "Against religious fanaticism" while chanting, "We are the people", a saying originally adopted by anti-communist demonstrators in the run-up to the fall of the Berlin Wall.

In Berlin, about 300 protesters were met with 5,000 counter-demonstrators marching with flags from the main left-wing parties.

And in Cologne, there were around 10 times as many people protesting against the anti-Muslim demonstrators.

In her New Year address last week, Ms Merkel urged Germans to turn their backs on anti-Muslim protesters, calling them racists whose hearts are full of hatred.

Speaking in the eastern town of Neustrelitz on Monday, she said: "We need to ... say that right-wing extremism, hostility towards foreigners and anti-Semitism should not be allowed any place in our society."

Justice minister Heiko Maas said at the Berlin counter-demonstration: "Germany is a country where refugees are welcome and the silent majority must not remain silent but rather go out onto the streets and show itself."

Germany has some of the world's most liberal asylum rules, partly due to its Nazi past, and the number of asylum seekers arriving in the country leapt to around 200,000 last year - four times as many as in 2012.