ICC chief executive Malcolm Speed told a news conference on Tuesday that the former Sri Lanka batsman would speak with the feuding captains during next week's third test in Perth. "We are bringing Ranjan in as a facilitator in an effort to prevent any ill-feeling that may have been present at the Sydney test from rolling over to Perth," Speed said in a statement.
"Ranjan is our chief referee and a highly respected figure within the game.
"He will remind the captains and other players of their responsibilities to conduct themselves in line with the Spirit of Cricket."
Cricket Australia chief executive James Sutherland had called on Ponting and Kumble to resolve their differences after an acrimonious end to last week's second test in Sydney.
Kumble evoked memories of Bill Woodfull's comment to the touring English side during the infamous 'Bodyline' series in 1932-33, by uttering the comment, "Only one team was playing within the spirit of the game."
Ponting defended the behaviour of his team mates, arguing that they played the game hard but fair but said he would be happy to meet with Kumble to try and resolve their differences.
Madugalle played 21 tests for Sri Lanka between 1982 and 1988 before retiring from the game. He joined the ICC as a match referee in 1993 and was made chief referee in 2001.
India have also threatened to quit the tour after spinner Harbhajan Singh picked up a three-match ban for making racially abusing Australia all-rounder Andrew Symonds.