Two men—an Iraqi and a Syrian—have been arrested on suspicion of murdering the German national.
The event coincides with a wave of racist populism in Europe.
Nearly six anti-refugee protests were staged every week in Germany in 2015.
One supporter reportedly shouted "Heil Hitler"
Christian Piquemal was one of dozens arrested across Europe during demonstrations in support of PEGIDA.
The German anti-Islam movement PEGIDA staged its biggest rally in months on Monday.
The anti-immigration group has said it will field candidates in next year's regional elections
Wilders offered to take Merkel back to the Netherlands with him, provoking chants of "Merkel must go!" from the audience at a demonstration by German anti-Islam movement PEGIDA.
A German study found that the majority of the population thought democracy was flawed in the country.
The news came just as supporters of PEGIDA staged a march in another the east German city, Leipzig.
Lutz Bachmann deleted the picture after being contacted by German media.
Anti-Islam group Pegida has been holding weekly rallies since October.
The PEGIDA movement indicates growing anti-Islamic sentiment in the wake of the Paris attacks
Merkel's words come hours before marches by anti-Islam group PEGIDA were due to start in several German cities.
Tommy Robinson endorsed German anti-Islam marches and said former EDL members have joined them
The organisers of anti-immigration marches across Germany seized on the terrorist attack in Paris
The grass-roots anti-Muslim movement has rapidly gained popularity and attracted condemnation from leaders
The number of attendees has been increasing week on week
This week Merkel's conservatives debated banning the burka, the full body covering worn by some Muslim women