Oil prices dropped over 2% towards its 11-year low on Tuesday, as traders shrugged off growing tensions between two of the world's biggest oil producers and focused instead on a stronger US dollar and swelling US crude inventories.

Relations between Saudi Arabia and Iran collapsed in acrimony this week after the Kingdom's execution of a Shiite cleric set off a storm of protests in Tehran. On Tuesday, Saudi state news agency reported that four armed men set on fire a bus transporting workers in the nation's oil-producing Eastern Province.

Instead of fanning fears of a disruption in supplies, however, some Organization of the Petroleum Exporting Countries delegates said the rift could exacerbate oversupply concerns by quashing already faint hope on a cut in output.

The oil market fell under additional pressure from a firmer US dollar, which gained 0.5% to hit a one-month high as traders sought safer havens, and signs of a further swell in already record US inventories.

Brent crude prices LCOc1 fell 80 cents to settle at $36.42 a barrel. Prices hit an 11-year low of $35.98 a barrel just before Christmas, capping a year where the benchmark's value dropped by more than a third.

US West Texas Intermediate (WTI) crude CLc1 slipped 79 cents to settle at $35.97 a barrel.

The discount for US WTI crude versus Brent CL-LCO1=R widened by some 25 cents after a report that BP Plc was planning work at a large crude unit at the 413,5000 bpd Whiting, Indiana, refinery, effectively backing more crude into the Cushing, Oklahoma hub.

US crude inventories fell 5.6 million barrels last week, American Petroleum Institute data showed. At Cushing, stocks rose 1.4 million barrels.

Prices pared losses by around 30 cents afterwards, but slipped again afterwards.

With so much production globally and healthy inventories, rising geopolitical risks appear muted, according to Matt Smith, director of commodity research at ClipperData.

"These two elements are serving as not one, but two security blankets for the market, assuaging any potential supply fears."

A Reuters survey found that OPEC oil output fell in December. Yet, OPEC production was pumping close to record amounts, signalling few signs that producing members were choosing to reign in output that has pushed prices to 11-year lows.

Iran said it was prepared to moderate its output and exports, once sanctions are lifted, to avoid pressuring prices, a senior National Iranian Oil Co official said.