Sri Lanka's World Cup captain has asked his predecessor to not just throw names.
Sangakkara challenges Tillakaratne to back his match fixing allegations
"Hashan has played the game for years and he's captained Sri Lanka as well. So it's interesting to see what he has to say and if he has anything more than allegations," Sangakkara was quoted as saying by the Press Trust of India news agency.
Tillakaratne, who played 83 Tests and 200 one-dayers during a 15-year career, claimed last week that Sri Lankan players had been involved in match-fixing since 1992 and added that he was prepared to name some of them.
Sangakkara, captain of the Deccan Chargers franchise in the Indian Premier League, said Tillakaratne should work with the International Cricket Council if there was any basis to his allegations.
"It's dangerous to throw names around," said Sangakkara, who quit as captain after Sri Lanka's defeat to India in the World Cup final last month.
"He should work very closely with the ACSU (Anti-corruption and Security Unit) of the ICC and the home authorities to ensure that something's done about it if there is any foundation to those claims.
"But beyond that I don't think it makes any big sense to the players playing now."
Tillakaratne's comments came as the sport tries to emerge from last year's spot-fixing scandal involving some of the top Pakistan players.
He had stopped short of suggesting the World Cup final was rigged although he expressed reservations about the selection of the Sri Lankan team.
The fresh ripple caused by Tillakaratne has prompted former Pakistan captain Imran Khan to ask the Interntional Cricket Council to intensify their efforts to stamp out corruption.
The cricketer turned politician told reporters during a visit to the Moin Khan cricket academy the ICC's anti-corruption and security unit needed to be more productive.
"I think specal measures are required like keeping a constant check on assets and accounts of players and giving the ACSU more authority to curb corruption," Imran said.
Imran's comments on corruption in cricket come a few days after former Sri Lankan captain Hashan Tillakaratne claimed in a television interview that match-fixing had been going on in his country since 1992.
The Sri Lankan cricket authorities have asked Tillakaratne to produce evidence to back up his claims.
Imran said it was very difficult to detect spot-fixing instances in matches, insisting other steps were required to meet the challenge of fighting corruption.
"It is very hard to detect such things and than find evidence to prove spot fixing has happened in a match," he said.
"But the more these instances are spoken about the more damaging it is to the sport's credibility."