However, a second statement made on Monday evening, also claiming to be from the Continuity IRA, has denied any involvement in the hotel attack.
It is understood four men were involved in Monday's attack, which happened at 19:45 GMT.
Speaking about the latest shooting, Irish Justice Minister Frances Fitzgerald said it was "another deplorable example of the ruthlessness of gangland criminals".
Image copyrightRTEImage captionIt is understood four men were involved in the attack and they fled in a Volkswagen Golf
"It seems that some gangs are intent on waging a feud where human life counts for nothing," she said.
"The gardai [Irish police] will take all necessary steps to try to prevent further bloodshed but we have to recognise the challenges they face. Members of gangs who have fears for their safety should come forward to the gardai."
Garda Commissioner Noirin O'Sullivan and senior investigators will hold talks with the minister on Tuesday.
Image copyrightRTEImage captionIrish police believe the killing could be a reprisal for the murder of David Byrne on Friday
He added: "Those behind this latest shooting, and those behind the dreadful attack last Friday at the Regency Hotel, must be apprehended and taken off our Streets."
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