"We now can not confirm there have been shots or deaths", Cologne police said on Twitter.
Authorities said the perpetrator has sustained life-threatening injuries.
The square and other areas surrounding the station were subsequently the scene of demonstrations against, and in favour of mass migration in response to the crimes.
Cologne police were forced to close parts of the German city's main train station because of a hostage situation.
Travellers were ordered to evacuate the large central station, which sits on Cologne's Dom Platz beneath the city's historic cathedral early Monday afternoon.
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Herlihy noted it's "quite rare" to suffer neurological complications like AFM, encephalitis and meningitis from enteroviruses. After the 120 cases in 2014, there were 22 in 2015, 149 in 2016, and 33 past year , according to the agency.
Police say officers have contact with the man and that trained hostage negotiators are working on the case.
Reports speak of at least one explosion during the incident. "The suspect is under control", Cologne police said.
COLOGNE, GERMANY - OCTOBER 15: Police stand outside Cologne main railway station on October 15, 2018 in Cologne, Germany.
It is understood that the hostage, believed to be female, has sustained "light injuries".
State rail operator Deutsche Bahn suspended all train traffic through Cologne, a major hub for rail travel through North Rhine-Westphalia state and nationwide. Police would not speculate on whether the hostage situation was terror-related.