Mercedes motorsport boss Toto Wolff and Force India deputy team principal Bob Fernley suggested the FIA should look at the rules imposed in the wake of incidents during the Austrian Grand Prix.
But McLaren team principal Eric Boullier has revealed FIA race director Charlie Whiting has no intention of either a relaxation in the rules, or at least opening it up for debate.
Boullier said: "There were discussions between the teams and the FIA, and seeking either more freedom or clarification, and the FIA has been clear they will not change their position."
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Nico Rosberg suffered a brake-by-wire failure on the penultimate lap of the race at the Red Bull Ring, compromising him in his last-lap battle with Mercedes team-mate Lewis Hamilton.
Sergio Perez crashed out on his penultimate lap when the brakes failed on his Force India, while team-mate Nico Hulkenberg retired several laps earlier due to his own brake issues.
In both incidents, neither Mercedes nor Force India were able to warn their drivers of the situation due to the enforcement of the radio ban.
Fernley was particularly outspoken, saying: "We've got to look at the radio communication bit because we were not allowed to tell the drivers their brakes were critical.
"It's a bit worrying. It seems a bit silly putting a halo on a car but not being able to tell a driver his brakes are about to go."
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