DUBAI, May 24 (Reuters) - Iran will abolish a motorists' allowance for heavily subsidised fuel and set a price, the deputy oil minister said on Sunday, as the government moves cautiously to cut back costly handouts.

"We have decided that petrol will be sold at a single rate of 1,000 tomans ($0.35) per litre," Abbas Kazemi was quoted as saying by the ISNA news agency, using a common measure of currency equal to 10 rials.

President Hassan Rouhani, elected in 2013 on a platform of better economic management, has championed efforts to rationalise pricing and pushed through a modest increase in fuel prices last year.

The government is trying to curb subsidies that have led to profligate energy consumption and put a strain on public finances, already squeezed by international sanctions and last year's drop in oil prices.

An Oil Ministry advisor on Saturday suggested that fuel subsidies could be lifted altogether, but the government appears to have decided to proceed more cautiously, as the new flat rate is still below market prices.

Iranians have grown accustomed to heavy subsidies, particularly in the energy sector, and there was widespread rioting in 2007 when an allowance was first introduced to limit motorists' access to the cheapest-priced fuel.

Reducing subsidies also threatens efforts to curb inflation, though the government's modest subsidy cut last year did not disrupt a downward trend that has seen inflation fall from 35 percent to 15 percent in the past two years.

The changes will take effect in mid-September, Kazemi said. Eligible motorists currently receive an allowance of 60 litres of petrol a month at 700 tomans ($0.24) a litre, and pay 1,000 tomans a litre for any additional consumption. ($1 = 28,650.0000 rials)

(Reporting by Sam Wilkin) ((sam.wilkin@thomsonreuters.com; +971 4453 6548; Reuters Messaging: sam.wilkin.thomsonreuters.com@reuters.net))

Keywords: IRAN SUBSIDIES/