The FBI is warning of a "frightening" new telephone scam: Callers claiming to have kidnapped a family member and demanding an immediate wire transfer for the person's release.

The requested ransom payments have varied between $600 and $1,900 so far, the FBI said in a statement released Tuesday. On some occasions, the "kidnappers" have sought additional payments -- even after an initial payment was made, the FBI said.

"This is a scheme that takes advantage of some of the most vulnerable in New York City," FBI assistant director-in-charge George Venizelos said, adding: "We need the public to be aware of this scam and call us if they have been a victim."

Police and the FBI said the scam works like this:

A person will call a resident claiming individuals "have kidnapped a family member" and demanding payment.

No actual kidnapping has taken place, the FBI said, and victim telephone numbers appear to be dialed randomly.

Sometimes, the caller might try to persuade the victim that a relative was in a serious car accident with a member of a gang and needs to be hospitalized, but tells the victim that injured person will not be taken to a hospital until funds are wired to repair a damaged vehicle, for example.

"Often the reason they are holding the alleged victim varies," the FBI said, "but some of the most prominent scams involve car accidents, drug debts, gang assaults or persons being smuggled across the border."

The key to the scam is that the callers often insist the money be transferred while the parties remain on the line.

During the call, the fake kidnappers might have "a young female scream for help."

Indications that a person might be a victim of such a scam, the FBI said, are incoming calls made from an outside area code (sometimes from Puerto Rico, with area codes 787, 939 or 856), calls that do not come from an alleged kidnap victim's phone, and involving callers who go to great lengths to keep a potential victim on the phone or prevent the person from calling or locating the alleged kidnap victim, and callers who accept ransom only by wire transfer.

Police and the FBI said the best way avoid being victimized by the scam is to try to slow the development of the situation, asking the caller to allow them to speak to the victim directly, and by attempting to contact the alleged kidnap victim by email or telephone while keeping the caller on the phone.

The number of people victimized so far was not clear.

The FBI is asking anyone possibly victimized by such a scheme to call them at 212-384-1000 or the NYPD at 800-577-TIPS. All calls will be kept confidential. The FBI asks anyone who believes they have been involved in a real kidnapping to call 911 or their local FBI office.