A group calling itself the IRA are claiming responsibility for the explosive devices which were sent to several Army Carers officers across England, police said.
Scotland Yard said the group claimed they were responsible for sending the packages to the army recruitment officers by contacting a Northern Irish media outlet using a recognised codeword.
The group also reportedly said they will continue to launch attacks "when and where the IRA see fit".
David Cameron held an emergency Cobra meeting after the "crude but viable explosive devices" were sent to offices in Oxford, Brighton, Canterbury and Slough.
A Downing Street spokesperson said at the time the packages "bore the "hallmarks of Northern Ireland-related terrorism". One of the packages was stamped with a Republic of Ireland postmark.
This followed packages which were sent to Aldershot, Reading and Chatham two days previously.
Met Police have now said a group calling itself the IRA is claiming the responsibility.
A spokesperson said: "We are aware of the claim of responsibility for the devices that were sent to army recruitment centres in England last week.
"The claim was received on Saturday, 15 February by a Northern Irish media outlet using a recognised codeword.
"The claim was allegedly made on behalf of the 'IRA'.
"The public is urged to remain vigilant and report anything suspicious to the Anti-Terrorist Hotline 0800 789 321 0800 789 321."
The Irish News reported that the group released a statement which said: "The IRA claims responsibility for the explosive devices that were sent to British armed forces recruitment centres in England. Attacks will continue when and where the IRA see fit."
The Irish government condemned those who sent the packages as "cowards" who are "hellbent on turning the clock back to the violence".
Democratic Unionist deputy leader Nigel Dodds said: "Those behind the deadly packages are to be condemned. Those who cling to terrorism should realise that it failed in the past and it will do so again. It will only lead to further hurt and suffering.
"Northern Ireland has turned a corner. We are moving forward and no-one wants to go back to the bad old days."