On Thursday local police chief Martin Kirchler told the Tiroler Tageszeitung that the authorities are confident of catching the perpetrators, who remain on the loose.
Chief police investigator Ernst Kranebitter said that the police have so far received 19 reports from women who were assaulted by the men, who are thought to be immigrants from Asia or North Africa.
The police investigation is examining CCTV footage, as well as questioning men living at local refugee reception centers who fit the description. The victims described the men as dark-haired, some were bearded, and one had a missing tooth.
"We will be grateful for any information we receive," Kranebitter told the press.
Kirchler responded to criticism of the police operation in Innsbruck on New Year's Eve. He said the number of police deployed in Innsbruck on New Year's Eve 2016 had increased to 90, in comparison with 60 the previous year. However, the police chief said that next year, the force will increase its surveillance of visitors arriving at the main celebrations.
As well as Innsbruck, Austrian women in Graz, Salzburg and Vienna also reported that they were victims of sexual assault on New Year's Eve.
Users of social networks were quick to draw comparisons between events in Austria and those in Germany a year earlier.
'#New Year's Eve in #Austria, #police in Innsbruck investigate sex attacks. Not Cologne, but Innsbruck,' wrote one.
''#Nafri (North Africans), a series of sex attacks in Innsbruck. The perpetrators are reminiscent of New Year's Eve in Cologne.'
Facebook users also commented on the news, and the controversial use of the term "Nafri" to describe North Africans.
"Instead of questioning whether we really have no choice but to unconditionally support people with highly questionable values, people would rather discuss whether the term "Nafri" is okay or not. Nothing good will come of that," wrote one.
"'All the perpetrators are thought to be of southern (foreign) appearance and under 30 years old….' no further questions," wrote another.
A year ago Cologne and other cities in Germany were rocked by a wave of sex attacks on women during public celebrations at New Year's Eve, committed by male perpetrators of Asian or North African appearance, believed to be migrants or asylum seekers. This year, police across Germany and other large European cities strengthened their numbers and security procedures, including screening of potential suspects.
On December 31 more than 1,000 young men of North African and Arab appearance gathered in smaller gangs around the main train station in Cologne and carried out a wave of sex attacks and robberies, directed against women. According to the Cologne prosecutor's office, more than 1,200 people were victims of crime during the event in the city last year, including 648 victims of sexual assault.
Similar outbreaks of criminality were recorded last New Year's Eve in other German cities, including Hamburg and Bielefeld. According to Germany's Federal Criminal Office, 1,200 women across Germany were sexually assaulted during public celebrations at New Year's Eve last year, and at least 2,000 men were involved in the assaults.