Muralitharan, 35, became only the second bowler after Australian Shane Warne to claim 700 Test wickets on Saturday as Sri Lanka hammered Bangladesh by an innings and 193 runs to sweep the three-match series.
Rajapakse, who was in Kandy town on official business, threw an informal celebratory dinner for Muralitharan at the presidential palace on Saturday night attended by both teams and officials.
Muralitharan, a Tamil, received a plaque from the president as tributes poured in for the master bowler who needs just nine more wickets to overtake the retired Warne's world record of 708 wickets.
Sri Lankan captain Mahela Jayawardene hailed Muralitharan as the best bowler in the world, a view shared whole-heartedly by the rest of the cricket-mad island nation.
"We were not surprised at all that Murali got to 700," said Jayawardene. "He is, after all, the best bowler in the world and is sure to set new landmarks by the time he quits.
"We will remember Murali not only for his record-breaking feats but also for the man he is. He remains as humble as before and is someone to be treasured for ever."
Muralitharan reached the 700-wicket mark the same day Tamil Tiger rebels killed at least 16 government soldiers in heavy clashes in northern Sri Lanka.
The rebels are fighting for an independent homeland for the Tamil minority on the Sinhalese-majority island, a 35-year-old conflict that has claimed more than 60,000 lives.
Muralitharan, meanwhile, set his eyes on taking 1,000 Test wickets and hopes to play for Sri Lanka till the 2011 limited-overs World Cup to be hosted in the Indian sub-continent.
"It is a big achievement but I think I can achieve a little bit more," Muralitharan said.
"I anyway knew I was going to get to 700. The challenge is whether I can take 1,000 Test wickets before I retire. I am now thinking about playing until the next World Cup."
Muralitharan, a veteran of 113 Tests who made his debut against Australia in 1992, said he had worked hard over the last 15 years to become one of the most feared bowlers in the game.
"So many years at the top takes a lot out of you but I am still hungry for wickets and that is what matters."
It took him just 12 Tests to move from 600 to 700 wickets.
Sri Lanka are due to tour Australia for two Test matches in November, but Muralitharan was unsure of becoming the leading bowler in Warne's backyard.
"Wickets there usually help fast bowlers, but I am more concerned about winning the series, something we have not done in Australia," he said.
It will be fitting if Muralitharan gets crowned in Australia where he has endured the most humiliating moments of his otherwise glittering career.
The off-spinner was controversially called for throwing by Australian umpire Darrell Hair during Sri Lanka's tour Down Under in 1995.
Two years later, another Australian umpire, Ross Emerson, called Muralitharan during a one-day series there, prompting a bio-mechanical analysis of his bowling action at the University of Western Australia in Perth.
The International Cricket Council cleared Muralitharan and his bowling action has since not been questioned by umpires around the world.