Wegner said officials received a ransom demand on Thursday evening. He did not disclose the amount, though Der Spiegel reports the hackers are demanding 30 bitcoin, worth around €2 million (£1.7 million).
The attack forced some of the city's online systems offline, disrupting services including housing benefit applications and payments for several days.
Investigators are working to determine the full extent of the breach. Officials said the initial data leak occurred between 7 and 12 August, and two department networks were shut down on 14 August. Subsequent forensic investigations revealed further data leaks within Berlin's transport and environment department.
"It cannot be ruled out that personal or other non-public data may also be affected," the mayor's office said in a statement.
The Rhysida group, which is thought to operate from Russia and eastern Europe, has reportedly taken responsibility. The group was also behind a previous attack on the British Museum, according to news reports.
Rhysida has said on its website that it intends to begin auctioning the 5.79 terabytes of data it was able to steal from Berlin in seven days' time, according to Reuters.
"Berlin will not be blackmailed," Wegner said. He said state police, prosecutors and federal security services were investigating the suspected perpetrators "with the utmost urgency," and that inquiries into the "content and scope of the compromised data are being pursued with great intensity."
Authorities have not officially named the suspected cyberattackers, though Der Spiegel is carrying a screenshot of the Rhysida group's dark web site claiming to possess files.