She conceded that there are no guarantees that the hackers will release the records once the payment has been made.
The council already voted to spend nearly $1m (€892,922) on new computers and hardware after hackers captured the city's system three weeks ago.
The Riviera Beach attack began May 29 after a police department employee opened an infected email attachment.
On June 3, city officials agreed to spend $941,000 on 310 new desktops and 90 laptops to rebuild its IT systems, but as the original data hadn't been backed up, a unanimous 5-0 vote took place this week that will see the council's insurance carrier pay the hackers 65 Bitcoin, around $592,000.
Spokeswoman Rose Anne Brown said Wednesday that the city of 35,000 residents -located just north of ritzy West Palm Beach - has been working with outside security consultants, who recommended the ransom be paid.
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The city's decision, as reported by CBS News, came after officials came to the conclusion that there was no other way to recover the city's files. The hacker specifically demanded payment in cryptocurrency bitcoin because the owner of the bitcoin account can't always be identified.
The FBI said on its website that it "doesn't support" paying off hackers, but Riviera Beach is not alone: many government agencies and businesses also pay ransom demands.
The hit on Riviera Beach is the latest in a series of worldwide attacks aimed at extorting money from governments and businesses.
The computer infrastructure of a number of United States cities has been targeted by hackers recently including that of Baltimore, which refused to make a ransom payment. Atlanta estimated that recovering from a sustained attack that debilitated the city a year ago could cost $17 million.
The men, who have not been arrested, received more than $6 million in payments and caused $30 million in damage to computer systems, federal prosecutors have said. He is also believed to have stolen $81m from a Bangladesh bank. Some of those were against individuals. The hackers encrypted the city's files, holding them for ransom and demanding a huge chunk of cash.
Liska said that while most ransomware that finds entry via phishing attacks stops at a single system, Ryuk attempts to propagate across the entire enterprise.