Carrying banners and signs bearing slogans like "Rapefugees not welcome", the far-right protesters took aim at Merkel, accusing her of allowing migrants to running amok in Germany through her liberal stance towards those fleeing war.
"Merkel has become a danger to our country. Merkel must go," a member of PEGIDA told the crowd, which echoed the call.
Witnesses have described the perpetrators of the assaults in Cologne on the night of December 31 as people with "North African or Arab" appearance.
"These women who fell victim will have to live with it for a long time. I feel like my freedom has been robbed from me," a mother of four introduced as Christiane told the rally.
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"That's impossible. Frau Merkel, Frau Reker, you are women! Where is your solidarity? What are women worth in this society?" she said, referring to Henriette Reker, who is mayor of Cologne, and who was stabbed in the neck last October by a man with a far-right background.
Some also heckled at the line of police officers standing guard, saying "where, where, where were you on New Year's eve?"
A chopper circled overhead, and an occasional firecracker went off, adding to tensions as leftist demonstrators staged a counter-protest.
Kept at bay from the PEGIDA crowd by police they chanted "Nazis raus!" (Nazis out!).
"There is nothing right about Nazi propaganda," said a slogan on the sign held up by one protester, while another read "Fascism is not an opinion, it is a crime".
Half a dozen Iraqi and Syrian refugees were also part of the counter-demonstration group.
PEGIDA started life over a year ago as a xenophobic Facebook group, initially drawing just a few hundred protesters to demonstrations in the eastern city of Dresden before gaining strength, peaking with rallies of 25,000 people.
But PEGIDA has seen a revival with the record influx of migrants to Germany.