Some 93 MPs have signed an early day motion demanding action, although the petition is not binding on government ministers.
It comes amid AA warnings that rising fuel duty is becoming a socially-divisive tax splitting the nation into the 'drives' and 'drive-nots' during the economic downturn.
Lower-income and rural drivers are losing mobility faster than better-off motorists, said the motoring organisation.
The AA has written to Chancellor George Osborne to urge him to revert back to the old system of setting annual fuel duty, which takes into account current economic and social conditions – not an automatic turning of the screw based on inflation.
The AA has also called on Mr Osborne to use the Consumer Price Index, not the Retail Price Index, as the inflation indicator for fuel duty considerations.
The Treasury needed to end the vicious circle of fuel duty increases pushing up RPI which can then boost the inflation rate for the next fuel duty rise, it said.
As it was, drivers already paid more VAT on fuel duty (adding 0.6p to the 3.02p duty increase on 1 January) rises at the pump.
AA president Edmund King said: "The private car is, for most people, a necessity not a luxury. It is their means to a job, health care, doing the shopping, visiting relatives and friends and also for improving the quality of their lives.
"We were disappointed that the January fuel duty rise went ahead at a time of rising oil prices and higher VAT. The AA firmly believes that business and households should be given a break from the annual cycle of fuel duty increases.
"Motorists do not understand the logic of high fuel duty rises which further increase RPI and force demand down at a difficult time for family and business budgets which need mobility to stay afloat.
"Although we fully recognise the need to balance the books we also believe the time has come for activity to be stimulated through lower pump prices."
Measuring how regressive fuel duty increases have become, AA/Populus research shows that less well-off drivers have suffered more since the price of fuel peaked at 137.43p a litre for petrol and 143.04p for diesel.
Petrol has since remained within 3p of that record.
Mr Osborne is due to give his Chancellor's autumn statement on 29 November.