The Formula One Teams' Association (FOTA) issued a statement on Friday questioning the validity of the rule change which will see the world championship handed to the driver with the most wins.
FOTA believes that the rules could not be changed at this late stage without unanimous support of the teams.
The FIA has responded to FOTA's claims, suggesting that its World Motor Sport Council that voted for the changes earlier this week was under the impression that the teams had supported the 'winner takes all' proposal put forward by Bernie Ecclestone.
In light of complaints from leading figures, the FIA has now said that if the teams are unhappy then the introduction of the wins systems will be delayed until 2010.
The statement said: "On 17 March, the FIA World Motor Sport Council unanimously rejected FOTA's proposed amendment to the points system for the Formula One Drivers' Championship. The 'winner takes all' proposal made by the commercial rights holder (who had been told that the teams were in favour) was then approved.
"If, for any reason, the Formula One teams do not now agree with the new system, its implementation will be deferred until 2010."