Top-selling German tabloid Bild and 50 prominent Germans called on Tuesday for an end to what they see as rising xenophobia, a day after thousands of protesters in several German cities rallied against Muslim immigration.

Monday's rallies, organised by a new grassroots movement called PEGIDA, or Patriotic Europeans Against the Islamisation of the West, have become a weekly event in the eastern city of Dresden.

Some 18,000 people, the biggest number so far, turned out in Dresden but similar rallies in Berlin and the western city of Cologne were heavily outnumbered by counter-protesters who accuse PEGIDA of fanning racism and intolerance.

Bild published a 'No to PEGIDA' appeal on Tuesday, covering the front page and a double page spread on page 2 and 3 with quotes from the 50 politicians and celebrities.

"(They) are saying 'no' to xenophobia and 'yes' to diversity and tolerance," Bild's deputy editor, Bela Anda, wrote in a commentary. "We should not hand over our streets to hollow rallying cries."

In Dresden, the PEGIDA protesters waved Germany's black, red and gold flag and brandished posters bearing slogans such as "Against religious fanaticism and every kind of radicalism".

One poster in Cologne called for "potatoes rather than doner kebabs", a swipe at ethnic Turks who at around three million represent Germany's largest immigrant community.

Germany has some of the world's most liberal asylum rules, partly due to its Nazi past. The number of asylum seekers arriving in Germany, many from the Middle East, jumped to around 200,000 last year — four times as many as in 2012.

German Chancellor Angela Merkel has urged Germans to shun the anti-Muslim protesters, saying their hearts are full of hatred and argued that hostility towards foreigners has no place in Germany..

In Cologne, home to a large Muslim population, there were 10 times as many counter-demonstrators as PEGIDA protesters. In similarly multi-ethnic Berlin, some 5,000 counter-demonstrators swamped around 400 anti-Muslim protesters, local police said.

Cologne Cathedral and Berlin's Brandenburg Gate switched off their lights to protest against the rallies.

PEGIDA has nonetheless shaken Germany's political establishment which some say could help the Eurosceptic party Alternative for Germany (AfD). But the AfD, dogged by internal power struggle, is split over how to deal with the movement.

Bild's campaign drew current and former politicians, celebrities and businessmen.

"(PEGIDA) appeals to hollow prejudices, xenophobia and intolerance," wrote former Social Democrat Chancellor Helmut Schmidt. "A look at our past and economic sense tells us Germany should not spurn refugees and asylum seekers," he added.

Others included Finance Minister Wolfgang Schaeuble, rock star Udo Lindenberg, 76-year old pop star Heino and former German soccer captain Oliver Bierhoff.