Jan 13 (Reuters) - Oil prices edged higher on Tuesday, as heightened concerns surrounding Iran and potential supply disruptions outweighed the prospect of increased crude supply from Venezuela.

Brent futures LCOc1 gained 28 cents, or 0.4% to $64.15 a barrel by 0101 GMT, hovering near a two-month high struck in the previous session.

U.S. West Texas Intermediate crude CLc1 rose 28 cents, or 0.5%, to $59.78, its highest since December 8 hit earlier in the session.

Iran, one of the biggest producers of the Organization of the Petroleum Exporting Countries, is facing its biggest anti-government demonstrations in years, drawing a warning from U.S. President Donald Trump of possible military action over lethal violence against protesters.

Trump is expected to meet senior advisers on Tuesday to discuss options on Iran, a U.S. official told Reuters.

The U.S. president said on Monday that any country that does business with Iran will be subjected to a tariff rate of 25% on any business conducted with the United States.

The developments matter for oil markets as Iran is a major sanctioned producer and any escalation could disrupt supply or add a geopolitical risk premium.

"Unrest in Iran has added about $3-4/barrel in geopolitical risk premium in oil prices, in our view," Barclays said in a note.

Markets are also grappling with concerns of additional crude supply hitting the market due to Venezuela's anticipated return to exports. Following the ouster of President Nicolas Maduro, Trump said last week the government in Caracas is set to hand over as much as 50 million barrels of oil, subject to Western sanctions, to the U.S.

Global oil trading houses have emerged as early winners in the race to control Venezuelan crude flows, getting ahead of U.S. energy majors.

Elsewhere, geopolitical tensions escalated as Russian forces launched attacks on Ukraine's two largest cities early on Tuesday, Ukrainian officials said, killing one person in the northeastern city of Kharkiv.

In the United States, the Trump administration renewed its attacks on the Federal Reserve, underscoring concerns in markets about the central bank's independence and adding to uncertainty about future economic conditions and oil demand.

(Reporting by Anushree Mukherjee in Bengaluru; Editing by Jacqueline Wong)

((anushree.ashishMukherjee@thomsonreuters.com;))