Captains Alastair Cook and Mahendra Singh Dhoni have been urged to desist from any further public comment about the spat involving James Anderson and Ravindra Jadeja, until the case has been fully heard.
The International Cricket Council issued a statement on Sunday requesting that "all relevant parties ... respect the judicial process".
Jadeja has already been fined half his match fee, a sum thought to be in the region of £3,000, for his part in the reported fracas in the Trent Bridge pavilion stairwell during the first Investec Test between England and India.
Anderson faces a Level Three charge, under the ICC's code of conduct disciplinary procedure, at a full hearing before judicial commissioner Gordon Lewis on Friday - the day after the scheduled conclusion of the third Test.
The scale of punishment available if he is found guilty of "abusing and pushing" the India all-rounder extends to the possibility of a four-Test ban.
Cook spoke out on the eve of the second Test at Lord's last week, describing the matter as a "mountain out of a molehill" - and then on Saturday Dhoni publicly divulged some of his eye-witness evidence of what happened in Nottingham, as well as describing Jadeja's punishment as "very hurtful".
The world governing body responded with a press release which read: "The ICC today urged all relevant parties to respect the judicial process in relation to the alleged incident that took place during the first Test at Trent Bridge, which has resulted in charges being brought against England's James Anderson and India's Ravindra Jadeja."
ICC chief executive David Richardson said: "England captain Alastair Cook and, more recently, India captain Mahendra Singh Dhoni have made public comments relating to the alleged incident that took place during the first Test at Trent Bridge, the latter of which is critical of and undermines the ICC disciplinary process.
"The ICC would also like to reiterate its full support of the process followed and respect for the decision made by (match referee) David Boon.
"ICC code of conduct hearings of this nature are, generally speaking, difficult processes to work through - with detailed legal submissions, witness statements and oral witness testimony.
"We are satisfied that Mr Boon carefully and comprehensively considered the evidence and submissions presented to him at the hearing, which included conflicting evidence from both sides, prior to making his decision.
"In legal matters such as this, the ICC takes extremely seriously its duty as administrators of the game.
"Therefore, I request all stakeholders to respect the process which remains ongoing and remind them of their duties to the integrity of the process and the sport so that we can focus on the game of cricket itself."