The Formula One drivers are locked in a row over safety with Max Mosley, the president of F1's governing body.
Mosley has not yet set a date to hold talks with drivers again
The Grand Prix Drivers' Association has accused Mosley of not taking its efforts to tackle safety seriously.
The comments came in a letter released after Mosley cancelled a meeting at Silverstone on Friday in which he was due to discuss safety with the drivers.
The GPDA said it was "disappointed not to receive the full support of the FIA president" on safety issues.
The row has arisen from the fiasco at the US Grand Prix, when the teams on Michelin tyres pulled out of the race on safety grounds.
The drivers' letter was drafted at the French Grand Prix last weekend, where the drivers decided not to release it. But Mosley's decision to cancel the Silverstone meeting prompted the GPDA to change its approach.
All the drivers - with the exception of Michael Schumacher and Red Bull's David Coulthard, Christian Klien and Vitantonio Liuzzi - have signed the document.
In the letter, the drivers mentioned a telephone conversation between Mosley and a director of the GPDA - known to be Coulthard - the day before last week's investigation by the FIA World Council into the US GP fiasco.
Mosley is understood to have made it clear during that conversation that he did not appreciate the drivers sending a document to the World Council backing the position of the Michelin teams at Indianapolis.
The statement added: "We were... concerned to learn that during the course of this telephone conversation, you suggested the FIA might withdraw support for the ongoing safety initiatives of the GPDA."
Mosley's decision earlier on Tuesday to cancel the Silverstone meeting with the drivers came after Coulthard was quoted criticising many of the rules the FIA has introduced in the last two seasons.
Coulthard said: "All these rules - qualifying, single lap and 10-place penalty - they are not designed to wreck races but they have."
FIA president Mosley said the Scot had "distorted the purpose of the meeting - it will now not take place".
Coulthard had used it as a pretext to "air his views" on the rules, he said.
The Scot's decision not to sign the GPDA letter issued on Tuesday will be viewed as a move to distance himself from public criticism of Mosley - he has always preferred to handle such issues away from the public eye.
But Williams' Mark Webber - a fellow GPDA director along with Schumacher and Toyota's Jarno Trulli - has backed Coulthard, insisting that it is important drivers have their say in how the sport is run.
"There are some concerns from the GPDA after Indianapolis," said the Australian.
"We work together, all the drivers. We are as one. Time will tell if the drivers are a voice when it comes to these matters.
"We don't want to run the sport but we are part of the whole deal. It's all about the drivers - the public come to see the drivers."
Mosley has now invited GPDA members to another meeting, in Monaco or Paris, when a convenient date can be found.