The group has been linked to more than 10 thefts carried out in Edinburgh over the past three weeks.
Each time, the suspects claimed to be police officers in order to search unsuspecting visitors' bags and steal cash.
The latest incident happened on Wednesday, when a woman and her daughter, on holiday from Chile, had more than £1,000 stolen from a bag.
The pair were approached by a man on Magdala Crescent, who handed them a camera and asked them to take a photograph of him.
Another two men soon approached and, stating they were plain-clothes police officers, produced a photo card with the word "police" on it.
They searched the bag of the man, who immediately complied, and then looked through a bag belonging to the Chilean tourists. They made off with a large sum of dollars and sterling.
Police Scotland have issued a description of the three suspects linked to the various crimes that have taken place this month.
The first is an Asian man in his late 30s or early 40s, 5ft 10ins and of medium build. The second man is also Asian, in his mid 40s, 5ft 7ins and of slim build.
A third suspect is said to be of Mediterranean appearance, aged 30 to 35, 6ft 2in and of medium build.
Detective Chief Inspector Stuart Houston said: "There is clearly a group of thieves operating in Edinburgh who are falsely presenting themselves as police officers in order to search the bags of unsuspecting tourists.
"These crimes are being carried out in streets across the city centre. Unfortunately the so-called 'officers' act so quickly that the victims are being duped into thinking the cash is still in their wallets or bags.
"We would urge members of the public to look out for men who are acting suspiciously, especially around tourists, and contact police immediately the minute they see something untoward."