The mass attacks on women in Cologne and other German cities on New Year's Eve have prompted more than 500 criminal complaints, with Cologne investigations focused largely on asylum seekers or illegal migrants from north Africa, police have said.The attacks, mostly targeting women and ranging from theft to sexual molestation, have prompted a highly-charged debate in Germany about its open-door policy to migrants and refugees, more than one million of whom came to the country last year.In Cologne, police said that 379 criminal complaints had been filed by individuals or groups, while police in Hamburg said 133 similar complaints had been lodged in the north German city. Frankfurt also registered complaints, although far fewer. The Cologne attacks also heated up debates on immigration in neighboring Austria and Switzerland."What happened in Cologne is unbelievable and unacceptable," Austrian Interior Minister Johanna Mikl-Leitner, a member of the conservative People's Party that is junior coalition partner to the Social Democrats, told newspaper Oesterreich.There had been a handful of similar incidents in the border city of Salzburg. "Such offenders should be deported," she said, backing a similar suggestion by German chancellor Angela Merkel.Swiss media contained numerous stories about sexual assaults on women by foreigners, fueling tensions ahead of a referendum next month that would trigger the automatic deportation for up to 15 years of foreigners convicted of some crimes.In Cologne, around 40 percent of the complaints included sexual offenses, including two rapes, police said, as a 100-strong force of officers continued their investigations. No one has yet been charged."There have been arrests and we will continue to make arrests," a spokeswoman for the Cologne police said on Sunday. She said police had increased the number of officers on patrol. "It is then to be determined whether or not these people were involved on New Year's Eve."In an earlier statement, the city's police had said the suspects in the focus of their investigation "come largely from north African countries" and the investigation "concerns largely asylum seekers and people who are staying in Germany illegally."Gathering evidence is difficult, given the chaotic and crowded scenes on the night, when police were overwhelmed by the mass assaults. The attacks triggered demonstrations in Cologne on Saturday, one of which was organized by the anti-Islam PEGIDA movement.The far-right has seized on the alleged involvement of migrants in the Cologne attacks as proof that German chancellor Merkel's welcoming stance to migrants is flawed.Some in that crowd threw bottles and fire crackers at officers, and riot police used water canon to disperse the protesters.Separately, police in North Rhine-Westphalia said that a man shot dead as he tried to enter a Paris police station last week wielding a meat cleaver and shouting "Allahu akbar" (God is Greatest) had lived in Germany.Police said he had an apartment in an accommodation center for asylum seekers in Recklinghausen, north of Cologne. The original information came from French security authorities.A German newspaper Welt am Sonntag reported that the man had painted the symbol of Islamic State on the wall of his flat.