Ferrari and Mercedes are pushing for the 2013 engine rules to be delayed, FIA president Jean Todt has admitted.
It emerged recently that the agreed 'greener' four-cylinder turbo regulations no longer had the support of all four of F1's current engine suppliers.
Subsequent reports clarified that only Renault is now fully backing the move.
The FIA announced last Friday that it will now stage "consultations" with the sport's stakeholders and then consider at the end of this month a new "implementation date" for the rules.
Todt told Spanish newspaper Diario Sport that he finds the situation frustrating.
"It is they who proposed the regulations, and the FIA who accepted them," Todt said.
"The proposal didn't fall from the sky; we had 11 meetings with all the representatives of those involved.
"When I talk to those responsible at Renault they tell me they will go out of F1 if this new engine does not come in 2013. When I talk to Mercedes and Ferrari they ask me to postpone the introduction for a couple of years.
"They are not against the rules but want them postponed. So in the coming days I will keep up the contacts personally to see where we are," he added.
Teams must agree to Bahrain calendar reshuffle - Mosley
The FIA will have broken its own rules if the Bahrain Grand Prix goes ahead in October without the teams' consent.
That is the claim of the governing body's former president Max Mosley, as the intrigue surrounding the rescheduled race in the troubled island Kingdom deepens this week.
Last Friday, the FIA - now led by Jean Todt - stunned the F1 world by announcing October 30 as the new date for the 2011 Bahrain Grand Prix, shunting India to an unprecedentedly-late December 11 season finale.
But Mosley told BBC Radio 4's Today programme on Tuesday that he thinks there is not "the slightest chance" the change will ultimately stick.
Indeed, Bernie Ecclestone is now pushing for a new vote of the World Motor Sport Council, while the F1 teams FOTA group is understood to have written a letter to the sport's authorities asking for the same.
Mosley, also opposed to Bahrain on political grounds, said: "Apart from anything else you cannot change the calendar in the way it has been proposed without the unanimous agreement of the teams.
"So until written agreement of the teams is forthcoming, you can't actually change the date. It can't be done," he said.
Todt vows to help push for French GP revival
Jean Todt has backed reports France could return to the Formula One calendar in future with a race to alternate annually with famous Belgian venue Spa-Francorchamps.
A French newspaper quoted Spa promoter Andre Maes on Sunday as saying he had been recently "asked about" an alternating deal by French officials.
"This may be interesting, so I am waiting for further news," he told the Journal du Dimanche.
Well-known French commentator Jean-Louis Moncet asked FIA president Todt about the reports on Monday and published his response in his Auto Plus column.
"As president of the FIA, I am not directly involved in organising the Grand Prix of France but as I am French I would like to see it regain its place on the calendar.
"I know that many people are involved and trying to find a positive solution, particularly at the highest levels of government, but for now we must leave them to address the problem.
"If we can give a final push, we will," added Todt.
"I have heard about the possibility of an alternation, but quite informally. So I don't have the information to be able to comment any further."
It is believed the venue most likely for the scheme is not Magny Cours, the scene of the last French grand prix in 2008, but Paul Ricard at Le Castellet, a circuit with close links to F1 chief executive Bernie Ecclestone.
"It is surely one of the best circuits in the world," the 80-year-old is quoted by sports.fr. "It would be ideal.
"If someone comes to me and says 'I have the money and need a circuit to organise a grand prix', even if they are from China, as long as we can race in France, I'll be happy," added Ecclestone.
The Journal du Dimanche said French prime minister Francois Fillon has appointed countryman and Renault team boss Eric Boullier to help with the efforts to revive the French GP.
Todt, Ecclestone wavering on Bahrain decision
The first signs have emerged that the rescheduled 2011 Bahrain Grand Prix actually might not take place late in October.
The FIA decided controversially last week to put the troubled island Kingdom back on this year's calendar despite fears about logistics, politics and security.
Teams have vowed to discuss the decision amid reports of continuing violence in Bahrain, while angry protesters are calling for a race-day 'Day of Rage'.
FIA president Jean Todt met with reporters in Barcelona late on Monday and acknowledged that the race might not take place.
"If we have clear evidence that there is a risky situation, this will obviously be taken into consideration," he is quoted by the BBC.
Also wavering is F1 chief executive Bernie Ecclestone, despite his earlier support for the rescheduling.
The Times quotes him as suggesting Bahrain should instead take the spot at the very end of the 2011 calendar so that F1 can assess before then if the situation in the Kingdom is actually "safe and well".
The newspaper said Ecclestone, a World Motor Sport Council voter, was not convinced by the report about the situation in Bahrain compiled after FIA vice-president Carlos Gracia's recent visit.
"Better that we move Bahrain to the end of the season and, if things are safe and well, then that is fine, we can go," said Ecclestone.
"If they are not (safe), then we don't go and there are no problems.
"We listened to that report from the FIA and that was saying there were no problems at all in Bahrain. But that is not what I am hearing and I think we can see that we need to be careful," added the 80-year-old.
The Telegraph said the Briton has written to the 12 teams urging them to also express their concerns and demand the World Motor Sport Council take a new vote.
Alex Wilks - chief of the Avaaz pressure group - is also questioning Gracia's conclusion that all is well in Bahrain.
"The main organisation that has provided this information (to Gracia), the Bahrain-based National Institute of Human Rights, is closely associated with the Bahraini government and it appears the FIA investigator failed to contact any of the other key human rights organisations on the ground," he said.
Yet another potential problem is that while the FIA statement last Friday said the World Council had "unanimously agreed" to reinstate Bahrain, this actually appears not to be the case.
There are reports there was not a formal vote at all, but just a show of hands, with team bosses Stefano Domenicali and Vijay Mallya among those who agreed.
It is believed formal unanimity is required for calendar tweaks, but when asked on Monday if this is the case, Todt answered: "I couldn't say precisely.
"Was it 25 hands? 27? I saw all the hands up and said, 'Ah, unanimous agreement'. I pronounced it. And nobody objected. No one said 'I abstained' or 'I voted no'," the Frenchman said.
Todt says one race to drop off 2012 calendar
Jean Todt says one race will definitely fall off the proposed 2012 calendar.
The governing body's World Motor Sport Council last week rubber-stamped a provisional schedule for 2012 featuring an unprecedented 21 race dates.
Among the scheduled events are season opener Bahrain and the inaugural US grand prix in Texas, but the only race marked 'subject to confirmation' was Turkey in early May.
It emerged recently that the Istanbul race will not take place next year because officials did not agree to a dramatically increased sanctioning fee demanded by Bernie Ecclestone.
Asked by Spanish newspaper Diario Sport if a record 21 grands prix will be held next season, FIA president Todt answered: "Absolutely not.
"There are 21 dates, but the championship will be 20 grands prix."
Asked if Turkey's conditional date means Istanbul Park is the one that will be dropped, the Frenchman said: "I don't know which one will go, but the championship will be 20 races."