Sri Lanka Cricket (SLC) president Mohan de Silva said he had asked the ICC to increase the tolerance limit to possibly 15 degrees.
The tolerance limits set by the ICC are five degrees for spinners, 7.5 for medium-pacers and 10 for pacemen.
"We have written to the ICC today (Wednesday) asking them to review the tolerance limits based on a scientific study of bowling action of all bowlers," de Silva said on Wednesday.
"We are not sure there should be one limit for a pace bowler and another for a spinner. A pace bowler can deliver a slow ball and a spinner can deliver a fast ball.
"What are the limits to be applied in this case is not very clear to us. We want a thorough review of all this."
De Silva said he had the backing of at least six other Test playing countries in seeking a change of the bowling rules. He, however, declined to name them, only saying that they were mainly "Asian".
He said Sri Lanka Cricket had assembled a team of lawyers to prepare a document for the ICC and the use of a large contingent of legal experts was to show the ICC "that we mean business".
De Silva said Sri Lanka's Prime Minister Mahinda Rajapakse dropped the idea of suing the ICC after being advised of the proper procedure to follow by the local governing body of the sport.
He said the premier's backing was crucial to defend Muralitharan, whose bowling action was proved to be beyond the limits imposed by the ICC.
Rajapakse had said that Muralitharan, the most successful bowler in Test history with 527 wickets, was a national asset and he would do everything within his power and that of the Government to defend the bowler.
Muralitharan, whose unorthodox action has seen him being no-balled for 'throwing' in the past, came under fresh scrutiny because of the 'doosra'.
The bowler was told in April that if he persisted with it he could face a year-long ban.
Muralitharan was sent to Australia to work on his action after he was reported by English match-referee Chris Broad following the third and final Test against Australia at Colombo in March.
ICC chief executive Malcolm Speed had already said that a report forwarded to him by Sri Lanka Cricket but compiled by the University of Western Australia, meant Muralitharan's 'doosra' could no longer be tolerated.
The report showed an initial straightening of the arm by 14 degrees which after remedial work was reduced to 10 degrees, still five degrees more than the level of tolerance for spinners.