During his campaign announcement speech in June, Trump said the Mexicans coming into America are "bringing drugs" or are rapists, before qualifying that "some, I assume, are good people".
In Cologne, 120 complaints have been filed for robbery, sexual abuse and rape after dozens of reportedly mainly North African and Arab-looking men attacked women at the city's main train station.
Police said investigators working with video footage have identified 16 young men - mostly of North African origin - who may be suspects.
Geir Moulson reported from Berlin.
He said three suspects had been identified, but police were yet to make any arrests.
But as Merkel pressed for an European Union solution to the worst refugee crisis to hit Europe since World War II, the incidents stoked resistance to her policies.
But Cologne's mayor said there was no reason to believe those behind the attacks were refugees.
Dr Merkel's remarks also increase pressure to resign on Cologne's police chief, Wolfgang Albers. Anti-immigrants group are capitalizing on this tragedy while German officials have not clarified if the attackers were indeed asylum-seekers - which means they are still at large while their victims are being blamed for going through something traumatic.
Quoting police sources, Cologne daily "Kölner Stadt-Anzeiger" said the officer leading the team at the station wanted the report to include mention of Syrians and asylum seekers, but the senior officer writing the police report decided not to, saying it would be "politically awkward."
Another, it says, tore up his residence permit before the eyes of police, and told them: "You can't do anything to me, I can get a new one tomorrow".
"The feeling women had in this case of being completely defenceless and at mercy is for me personally intolerable and so it is important that everything that happened must come out into the open", she said.
Right-wing parties in Germany, including the Alternative for Germany (AfD), have jumped on the events to renew calls for a limit on the number of refugees allowed into Germany and for Merkel to close the country's border.
In the same report, a man reportedly tore up his asylum papers in front of a police officer, though it can not be confirmed if it was a real document. "(Chancellor Angela) Merkel invited me".
A leaked German police report on the Cologne New Year's Eve sex attacks has revealed chaos "beyond description".
While officials have cautioned against casting suspicion on migrants in general, the attacks have been seized on by some opponents of Germany's welcoming stance toward those fleeing conflict after the country registered almost 1.1 million asylum-seekers past year.
Police have recieved 53 complaints of harrasment relating to new years eve so far, including 39 of sexual harassment.
German weekly Die Zeit contrasted the violence in Cologne with the feel-good scenes in Munich four months ago when locals greeted arriving refugees with cheers, food and blankets.
Cologne's Mayor HenrietteReker, whose very bad response kept the universal culture of victim blaming alive, said women should stick to a code that would require them to stay "an arm's length distance from strangers".
"We heard a woman screaming and crying somewhere in the midst of this crowd, appearing to be escaping from a foreign man, who was shouting back and pointing his finger at her and chasing her with his accomplices", she wrote.