In Cologne, where most of the attacks took place, a police spokesman confirmed Chief Wolfgang Albers was fired Friday. Albers' dismissal comes amid criticism of his department's handling of the violence.
One victim of the Cologne violence told CNN there were too few police on the streets to prevent attacks.
"We ran to the police. But we saw the police were so understaffed," the victim said. "They couldn't take care of us and we as women suffered the price."
Spiegel Online reported that groups of men prevented officers from reaching those crying out for help.
Interior Minister Thomas de Maiziere has slammed the response of Cologne police while German Justice Minister Heiko Maas was among many who blasted Cologne Mayor Henriette Reker for advising women to keep "more than an arm's length" from unknown men.
Reker later complained the comments were taken out of context.
Cologne police spokeswoman Christoph Gilles told reporters Friday that some 170 criminal complaints have been filed related to the apparently coordinated attacks, "at least 120 of which have a sexual angle."
An 80-person investigative team is looking at 250 videos (with about 350 hours of footage), Gilles added.
The suspects include nine Algerian nationals, eight people from Morocco, five from Iran and four from Syria, German interior ministry spokesman Tobias Plate said. Two are German citizens, while one each are from Iraq, Serbia and the United States.
Other German cities had similar attacks that same night, including the northern city of Hamburg, where more than 50 similar incidents were reported.
Other European cities also reported attacks.
Police in Kalmar, Sweden, said Friday they had arrested two men described as refugees who only spoke Arabic or Kurdish. The men, who have since been released on bail, are suspected in two of the 11 sexual harassment complaints received in the town on New Year's Eve, according to police spokesman Johan Bruun.
Police are looking for 10 to 15 additional suspects who allegedly encircled a group of women in Kalmar and groped them, Bruun told CNN.
In all, 16 females between 17 and 21 said they were molested, he said.
In Salzburg, an Austrian city on the German border, two men have been charged with sexually assaulting women on New Year's Eve and New Year's Day, police said in a statement.
A 23-year-old Syrian citizen was arrested in the city's Old Town section on New Year's Eve after sending fireworks in the direction of a 17-year-old student, police said. She was slightly injured in her abdomen. Further investigation revealed he allegedly had sexually abused a 20-year-old from Bayern in the inner city before the fireworks incident, police said.
A 28-year-old Afghan allegedly sexually abused a 58-year-old woman in the early hours of January 1, police said.
Another woman reported she was sexually harassed on New Year's Eve by two men who also stole her phone, police said. A 24-year-old Afghan man was arrested and accused of molesting a 26-year-old January 6 at a downtown Salzburg pub, police said.
In Zurich, Switzerland, six women told authorities they were "robbed from one side, [while] being groped ... on the other side" by groups of men described as having dark skin, according to a Zurich police statement released Friday.
And in Helsinki, Finland, police said they are investigating two possible criminal offenses related to New Year's Eve harassment centered around "a gathering of asylum-seekers."
Both the Zurich and Helsinki allegations became public well after the incidents took place.
Critics had chastised authorities and media in Germany for not being upfront earlier about the attacks there -- though that news did get out sooner, spurring anti-migrant protests and challenges of Chancellor Angela Merkel for her openness to refugees from war-torn nations like Syria and Iraq.
Maas, the German justice minister, said Thursday that anyone convicted of such crimes could be deported
if they were seeking asylum.
"The law allows for people to be deported during asylum proceedings if they're sentenced to a year or more in prison, and that's possible with sexual offenses," Maas said.
Germany's embrace of migrants challenged
The idea that some refugees fleeing poverty and violence would commit crimes in the countries that welcomed them has spurred anger across Europe and calls for action.
Merkel has been praised
in many circles for her not only urging Europe to find a place for such migrants, but backing up her words inside Germany. The nation took in about 800,000 migrants last year, far more than any other European nation.
But critics have questioned the ability of so many migrants, predominantly Muslims, to suddenly adapt to a European way of life, and the apparently coordinated attacks in Cologne and elsewhere in Germany have fueled that sentiment.
Slovakian Prime Minster Robert Fico called for a summit of European Union leaders to discuss the refugee situation, and said "the idea of a milticultural Europe is unrealistic."
"It's a fiction, it's a dream. Simply, it doesn't work," he said.
While officials warned against scapegoating all migrants, Merkel herself has been vocal in slamming the "intolerable" attacks and indicating her government will send a "clear sign" to those who don't respect German law.
She also suggested what happened New Year's Eve may be symptomatic of a broader problem with regards to endangering women.
"I don't think these are single cases," Merkel said Thursday. "People have a right, and we as a state ... have the obligation to give the right answers to this."