More than $4 million have been lost by victims of phone scams since March, the police said yesterday.
In most cases, the callers impersonate overseas officials who tell potential victims that parcels containing illegal items had been shipped in their names.
Victims are told they must remit money to overseas bank accounts as a fine or a bribe, The Straits Times learnt from those who received such calls.
The police said they had more than 50 reports since March from people who were duped, and hundreds of alerts from concerned members of the public who received the calls.
They said the scam is very similar to fraud cases in Hong Kong and China over the last year.
It is believed the scam originated in China.
In recent cases, scammers have impersonated officers from the Singapore Police Force or staff from local courier companies such as SingPost.
Victims might also receive calls with fake local numbers, informing them that the parcels were delivered to local addresses, making the ruse more believable.
Some have been asked to visit a webpage where they can enter personal information, including details of their online banking accounts.
A 45-year-old lecturer, who declined to be named, told The Straits Times she received a call on Tuesday from an unknown local number. After responding to the automated message about an undelivered parcel from DHL, she was redirected to a man speaking Mandarin who claimed to be a DHL staff.
He told her that the Shanghai police had confiscated illegal goods she had taken to the airport there, and asked for her English and Chinese names.
As she had been a victim of credit card fraud last year, her suspicions were raised.
She recalled: "At first it seemed authentic, but I became suspicious as I had not travelled to Shanghai.
"Also, I have never made online transactions using my Chinese name, so I hung up."
Another woman received a call from a Mandarin-speaking woman who claimed to be a SingPost staff.
The self-employed 31-year-old, who wanted to be known only as Ms Soh, said: "I was alarmed because she knew my name and IC number.
"The woman told me I had used SingPost to mail illegal items to Shanghai and insisted that I talk to Shanghai police."
Ms Soh hung up.
A spokesman for DHL said it was first alerted to the scam in early April and now receives more than 200 reports daily.
The courier company filed a police report on April 8 and sent out an e-mail alert to customers.
It also posted an advisory on its Facebook page.
SingPost also said it was aware of the scam.
"We have been on high alert for scams and frauds using the SingPost brand name," said a spokesman. "We have also assisted the authorities in creating awareness through posters in our post offices and the distribution of scam awareness brochures."
FedEx declined to comment.
The Straits Times understands the scammers have even called the police as the phone numbers are computer-generated.
Police advised members of the public to ignore unsolicited calls and callers' instructions to transfer money.
"No government agency will inform you to make a payment through a telephone call, especially to a third party's bank account," said the police advisory.
"Do not provide name, identification number, passport details, contact details, bank account or credit card details to the callers. Such information is useful to criminals."
Those with information related to such crimes can call the police hotline on 1800-255-0000, or dial 999 for urgent police assistance.