Jean Todt (right) has asked Bernie Ecclestone to revise the 2011 calendar
The race was originally due to open the Formula One season in March, but was called off amid the political unrest and put back to October.
Earlier this week, F1 president Bernie Ecclestone said the Bahrain race could not go ahead as teams had objected.
Any change in the calendar required unanimous agreement from the teams.
Bahrain circuit chairman Zayed Alzayani said in a statement: “Whilst Bahrain would have been delighted to see the Grand Prix progress on October 30th… it has been made clear that this fixture cannot progress and we fully respect that decision.
“We want our role in Formula One to continue to be as positive and constructive as it has always been, therefore, in the best interest of the sport, we will not pursue the rescheduling of a race this season.”
The race in the Gulf kingdom was initially due to open the season in March.
But it was called off in February because of pro-democracy protests in which more than 20 people died.
After giving Bahrain months to decide whether it was in a position to hold the race, the governing International Automobile Federation (FIA) announced last Friday that it would be rescheduled for 30 October.
The FIA said civil unrest in the country had stabilised.
But the decision outraged human rights campaigners, and nearly half a million people signed an online petition demanding a boycott of the Bahrain race.
Cancellation was seen as inevitable since any change in the calendar required the unanimous written agreement of the teams.
They had written to the FIA and the commercial rights holder – Bernie Ecclestone – to express their opposition to the move.
The inaugural Indian Grand Prix – which had been provisionally moved to December to accommodate Bahrain – will now revert to the original 30 October slot.
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