No one was injured in the blast that occurred after a delivery vehicle was hijacked and the driver forced to take it to the police station.
It was the latest sporadic attempt by militant groups to target police officers, almost 30 years after a peace deal largely ended sectarian violence in the region.
The New IRA is one of a small number of active militant groups opposed to the 1998 peace deal.
It has been behind many of the attacks on police, including a similar attempted car bombing at a police station outside Belfast in March.
The targeting of police officers at their homes would be an escalation of those attacks.
The last officer to be killed in Northern Ireland, constable Ronan Kerr, died when a bomb exploded under his car outside his home 15 years ago.
The dissident group rejects the political compromises at the heart of the Good Friday Agreement that Northern Ireland will remain part of the United Kingdom unless a majority of the region votes by referendum to unite with Ireland.
The organisation said in a statement, which the Irish News said it received and included a codeword to confirm its veracity, it had intended to kill police coming out of the station after the driver was told to shout that there was a bomb in the car as they left.
"It is our intention, if they keep harassing the republican people, to bomb them (police officers) in their own houses, with no warning," the statement said.
The New IRA, a far smaller organisation than the Irish Republican Army (IRA), which disarmed after the peace accord, typically claims responsibility for any attacks in coded statements to local newspapers.
