His comments came as hundreds of republicans attended a ceremony in memory of fellow bomber Thomas Begley, who died when the device he was carrying exploded prematurely.
Nine Protestant civilians, including two children aged seven and 13, also died in the attack at Frizzell's fish shop on October 23, 1993.
"It was an IRA operation that went tragically wrong," Kelly told the event in North Belfast this afternoon.
He said the loss of civilian lives "was not the intention of the IRA".
There can be no excuse for the loss of innocent lives, he added.
"I am truly sorry for the loss of life and the injuries that were suffered that day, and for the suffering the families have endured," he said.
Kelly received a total of nine life sentences for his role in the attack but was released early in July 2000, under the terms of the Good Friday Agreement.
The plaque was unveiled by Begley’s father, Billy.
It states that Begley “died on active service” and is “always remembered by his many comrades and friends”.
Mr Begley said there was no intention to cause offence by holding the commemoration, saying he understood the pain felt by victims’ families.
A PSNI helicopter hovered above throughout the 20-minute ceremony.
A loyalist protest against the event took place nearby on the Crumlin Road.
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