"This will not be an isolated incident," a man claiming to be a spokesman for the dissident republican group said in a statement to the BBC.
"CIRA units have been authorised to carry out further operations. More drug dealers and criminals will be targeted," said the spokesman, who the BBC said had provided a code word to back up his claim.
One man, identified as 33-year-old David Byrne, was killed and two others were injured in Friday's shooting at the Regency Hotel in north Dublin.
The police had said they believed the shooting was the result of a feud between organised crime gangs.
Contacted by AFP, they declined to comment following the claim of responsibility by the Continuity IRA.
But lawmaker Gerry Adams, president of the Sinn Fein party once closely identified with the Provisional IRA, dismissed the claim.
"I understand a group calling itself the Continuity IRA has claimed responsibility for the attack at the Regency Hotel. They are not the IRA," Adams said in a statement to press.
Justice minister Frances Fitzgerald defended the police, when asked why crime journalists had been there but police officers had not.
"Let's be in no doubt as to who is to blame for this. The responsibility lies with the evil men who went into that hotel in broad daylight with AK-47s," Fitzgerald said, according to the Irish Mirror.
Irish police have set up checkpoints on roads amid fears of retaliatory attacks and have sent out armed patrols.
The police said at least six people were involved in the shooting -- three of them uniformed and helmeted and carrying automatic weapons.
