"These toys typically contain sensors, microphones, cameras, data storage components, and other multimedia capabilities-including speech recognition and Global Positioning System options", the agency wrote in the advisory, cautioning that certain toys could be hacked to record video and audio of children without their parents' knowledge.
Security failures were discovered in the Furby Connect, i-Que Intelligent Robot, Toy-Fi Teddy and CloudPets.
It has written to retailers asking them to stop selling the toys ahead of Christmas until the security problems have been resolved.
The hacks have a limitation: a stranger would have to be within Bluetooth range, or about 32 feet, of the toys.
The consumer group Which? checked popular connected toys to test their vulnerabilities.
The toys effectively speak and play with children based on messages transmitted over the airwaves through tiny Bluetooth or Wi-Fi aerials.
All four products pair with a smartphone over a Bluetooth connection to relay data.
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"That person would need hardly any technical know-how to "hack" your child's toy", the report states.
This could mean using pins or passcodes when pairing devices and encryption for any data that is transmitted.
Bluetooth is typically limited to a distance of 10 metres, meaning that any immediate threat is likely to be from someone nearby.
The connection could be made via a smartphone or laptop, opening up opportunities to control the toy. Researchers were then able to upload a custom audio file to the toy, which could be anything given the lack of restrictions, including inappropriate material.
CloudPets toys, on sale at Amazon, are stuffed animals that enable friends to send a child messages that are played on a built-in speaker.
Smart toys can be an appealing gift idea, but be careful: the Bluetooth connectivity in some products can make them easy to hack, according to a consumer watchdog. The Bluetooth feature lacks any authentication protection, however, meaning hackers can send voice messages to a child and receive answers back.
Consumer group Which? said an investigation found "worrying security failures" with the I-Que Intelligent Robot, Furby Connect, Toy-fi Teddy, and CloudPets (pictured) cuddly toy.
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Managing director Alex Neill said: "Connected toys are becoming increasingly popular, but anyone considering buying one should apply a level of caution".
After conducting a thorough investigation on how these toys work, the review site claims that some of them have "proven" security flaws. "If that can't be guaranteed, then the products should not be sold".
Vivid Imagination, who creates the i-Que toy, said it hasn't seen any reports of the toy being manipulated.
The FBI suggests that adults research any Wi-Fi or Bluetooth-enabled toys before giving them to a child, and that if they do have them, to take proper measures to secure them.
Hasbro, which makes the Furby Connect, said: "Children's privacy is a top priority, and that is why we carefully designed the Furby Connect and the Furby Connect World app to comply with children's privacy laws".
"A tremendous amount of engineering would be required to reverse-engineer the product as well as to create new firmware", it said.
The British Toy and Hobby Association said in a statement that it will monitor these toys to ensure that they're safe.
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