Kumble, in Dubai for a talk-show of a private broadcaster, said Muralitharan, who overtook the record for the highest number of Test wickets last week, was undoubtedly the "number one" bowler in the world.
"I think he is the number one Test bowler in the world at this point of time. All the controversy around him is unfortunate and unnecessary," the 34-year-old was quoted as saying in local daily Khaleej Times.
"Whatever needed to be done should have been done much earlier. You can't keep pointing fingers at Murali every time he takes a wicket," said the bowler who has picked 397 wickets in 84 Tests.
The ICC's Cricket Committee-Playing which is chaired by the legendary Sunil Gavaskar, is deliberating on illegal bowling action at a meeting which began in Dubai on Thursday.
Muralitharan, who has been banned from bowling his "doosra" the delivery that spins away from the right handers, has reportedly said that he may continue bowling it as he felt the ICC was discriminating against him.
Kumble brushed aside speculation that he was planning to quit One-day cricket to concentrate on Tests, saying, "I don't think there is any truth to it (speculation). I am not considering any such thing."
The Karnataka leggie also sought to put behind the disappointment of not being the first choice bowler during the 2003 World Cup final.
"As a team we did really well in the World Cup, but unfortunately we couldn't cross the final hurdle. Yes, it was disappointing not to be a regular in the World Cup, but I stuck to the task and am happy with my performance over the past season," said Kumble who had a remarakable run in the last season, taking 48 wickets from eight Tests.