Muralitharan, who broke Australian Shane Warne's world record for most Test wickets by taking his 709th against England in Kandy on Monday, has faced criticism in the past over the legitimacy of his bowling action.

"I don't think it's appropriate to criticise," Cricket Australia chief executive James Sutherland told a news conference.

"I think at a time like this we should be lauding the great feats of Muttiah Muralitharan and the fact that he's broken the record and shown incredible performances over a long period of time to be the number one wicket taker in Test history."

Sutherland noted that Warne did not be grudge Muralitharan the record and said the Australian's demotion to No.2 on the all-time list did not detract from his success.

"I don't think it's appropriate to compare, we're talking about two of the great bowlers of all time," he said.

"Murali is now the number one but that doesn't in any way diminish the achievements of Shane Warne and what he did.