In a statement provided to a local newspaper, the group said it placed the car bomb which detonated in Bishop Street shortly after 8.10 pm on January 19.
The statement to the Derry Journal read: “We also caution those who collaborate with the British that they are to desist immediately as no more warnings will be given.”
The group added that it will “continue to strike at crown forces and personnel and their imperial establishment”.
“All this talk of Brexit, hard borders, soft borders, has no bearing on our actions and the IRA won’t be going anywhere.
“Our fight goes on.”
The bomb and subsequent security alerts in the city were initially linked to a group called the New IRA, and police said investigating this group would be their “main line of inquiry”.
Days after the car bombing, the PSNI released CCTV footage that showed a group of young people pass the car shortly before it exploded in Bishop Street.
Officers described it as a “miracle” and “sheer luck” no one was harmed.
Police were given a 15-minute warning to evacuate the area before the bomb went off.
Local residents, including those in a sheltered housing complex for elderly people, were evacuated.
The days that followed saw a number of security alerts in the city where two vehicles were hijacked at gunpoint, a third was stolen and abandoned outside a school, and hundreds of residents were evacuated from their homes.
Five men were arrested on suspicion of the car bombing but were later released unconditionally.