FIA President Max Mosley says there still could be a breakaway Formula One series.
Mosley wrote that F1 is going through a 'difficult period' in a letter to the World Motor Sport Council to clarify details of a peace pact with the Formula One Teams Association.
Mosley dropped the contentious voluntary budget cap last Wednesday.
He insisted he wasn't bullied into submission by the eight rebel teams - including Ferrari and McLaren - but accepts it is an uneasy truce.
"This may well result in short-term problems in Formula One," Mosley said.
"It is possible FOTA will set up an independent series. That is their right, provided they do so under the International Sporting Code. But the Formula One world championship will continue to be run by the FIA as it has been for 60 years.
"The championship has had difficult times in the past, and no doubt will again in the future. But, that is no reason to hand control to an outside body."
Despite saying he would 'step back' ahead of October elections for his successor, Mosley now says he will fulfil his role as president until his fourth term in office ends.
In a letter to the FOTA, Mosley said he was keeping his 'options open' about whether to stand again after being angered by Ferrari president Luca di Montezemolo branding him a 'dictator'.