So far, officers have received nine reports of housebreakings in Forfar, Carnoustie, Arbroath, Dundee, Perth and Bankfoot which happened between Saturday, December 4 and Monday, December 13.
On each occasion, a number of men broke into the homes and stole a significant quantity of high-value items, including jewellery and cash.
The incidents are being treated as linked and the extensive enquiry also involves Tayside officers liaising nationally with members of other forces who are investigating similar housebreakings.
Detective Inspector Simon Murray said that all information, now matter how small, could help the investigation.
He said: “I’d like to reassure our communities that these break-ins are being thoroughly investigated and we continue to appeal for any witnesses to come forward.
"Local officers have been carrying out dedicated patrols throughout the affected areas.
“If you believe you have any information or witnessed anything suspicious, for example vehicles, possibly Transit vans or a silver Audi A3 touring about the area without purpose, then please speak to police.
"Any detail, no matter how small, could help with our investigation.
"Likewise, if you have private CCTV or dash-cam footage that shows anything suspicious, that could also assist with our enquiries.”
Anyone who can help with the investigation is asked to contact Police Scotland on 101. Alternatively, call the charity Crimestoppers anonymously on 0800 555 111.