A group calling itself the IRA says it was behind the parcel bombs sent to three London transport hubs and the University of Glasgow last week, according to police.
Officers say the group claimed five devices were sent but only four have been found so far.
Police Scotland and the Metropolitan Police have said the claim was received by a Northern Ireland media outlet using a recognised codeword.
The forces said in a joint statement it was allegedly made “on behalf of the IRA”.
Officers were already exploring this as a line of enquiry after the packages bore similarities to devices sent by Northern Ireland dissident groups in the past.
But police added they are keeping “an open mind” in their investigation.
The Provisional IRA, which was behind a 30-year campaign of violence, has been on ceasefire for more than 20 years.
But a number of dissident republican terror groups have claimed the mantra of the Irish Republican Army.
Sky’s senior Ireland Correspondent David Blevins said: “For example, the so-called ‘Real IRA’ bombed Omagh in 1998, claiming the lives of 29 people, one of them a woman pregnant with twins.
“More recently, an umbrella group calling itself the ‘New IRA’ has carried out a number of attacks, including the car bombing in Derry at the end of January.
“It is highly likely that any group using the letters ‘IRA’, to claim responsibility for last week’s parcel bombs, is a dissident republican group, opposed to the Northern Ireland peace process.”
Parcel bombs were sent to Waterloo Station and buildings near London City Airport and Heathrow Airport on Tuesday 5 March.
The devices were small, and while the package Heathrow was opened, there were no injuries.
A controlled explosion was carried out on a further suspicious package that was found at the University of Glasgow the next day.
At least three of the packages had Irish stamps with red hearts on them.
A package was also found at Parliament but was later deemed to be non-suspicious.
Those who have claimed they were behind the packages have suggested that five devices were sent.
The police joint statement said: “At this time, only four devices have been recovered.”
It added: “Extensive advice has already been issued to relevant businesses and sectors to be vigilant for and report suspicious packages to police.
“This advice was previously sent to armed forces personnel and is being reiterated again in light of this claim.
“We continue to urge the public to remain vigilant and report anything suspicious to police.”