The devices, which are said to bear similarities to those sent by dissident groups in the past, were found at three buildings in London and at Glasgow University.
In a joint statement, the Metropolitan Police and Police Scotland said a claim of responsibility was received on Monday by a media outlet in Northern Ireland outlet using a recognised codeword.
Police said the claim was allegedly made on behalf of the “IRA”.
Officers are said to have already been looking at this line of enquiry.
The police statement said those claiming responsibility had indicated five devices were sent, when only four devices have been recovered.
The first device was discovered at 9.55am last Tuesday at the Compass Centre in Hounslow and was opened by staff, causing it to initiate and burn the packaging it was sent in.
Around two hours later, British Transport Police were called to reports of a suspicious package in the post room at Waterloo Station. Specialist officers attended and made the device safe.
A third package was discovered at 12.10pm at London City Airport. Specialist officers again attended and made the device safe.
The following day, a fourth package was received at Glasgow University, where several buildings were evacuated as a precaution. A controlled explosion was carried out.
Detectives from the Met’s Counter Terrorism Command are leading the investigation into the three packages received in London, while Police Scotland is leading the investigation in Scotland.
Police said no arrests had been made.