"I would say it is a great tragedy, a monumental historical tragedy for which we deeply regret and we call upon the government of India and people of India to be magnanimous to put the past behind," Anton Balasingham, the chief negotiator for the Liberation Tigers of Tamil Eelam (LTTE), said in an interview with India's NDTV news channel.
Rajiv was killed in protest at India's involvement in Sri Lanka's civil war. Indian soldiers were sent to the north of the island as peacekeepers in 1987.
They ended up fighting with the Tigers and withdrew in 1990.
The Tigers have admitted their role in the attack before but this is the strongest expression of regret from the separatists.
Rajiv was killed by a suicide bomber while campaigning for his Congress Party in the run-up to national elections.
Fourteen other people were also killed in the attack in the town of Sriperumbudur, near Chennai [formerly Madras], the capital of the southern state of Tamil Nadu.
The Tigers have pledged not to work against India's interests, Balasingham told NDTV, saying India should be "actively involved in the peace process".
The LTTE fought a civil war against the Sri Lankan government which lasted nearly two decades. They want to create an homeland for ethnic Tamils in the east of the country.