By Sonali Paul

MELBOURNE (Reuters) - Oil prices rose on Tuesday after two days of losses, with some risk appetite returning as the market awaited clues from the U.S. Federal Reserve chairman on potential rate rises and as some oil producers continued to struggle to beef up output.

Brent crude futures gained 26 cents, or 0.3%, to $81.13 a barrel at 0156 GMT, after dropping 1% in the previous session.

U.S. West Texas Intermediate (WTI) crude futures rose 30 cents, or 0.4%, to $78.53 a barrel, after falling 0.8% on Monday.

A weaker U.S. dollar helped support oil prices on Tuesday, as it makes oil cheaper for those holding other currencies.

Oil price declines over the previous two sessions had been driven by worries about soaring cases of COVID-19 around the world potentially sapping fuel demand.

However, analysts pointed to tight supply from the Organization of Petroleum Exporting Countries, Russia and allies, together called OPEC+, not keeping up with demand and supporting prices.

"The market could still benefit from tighter supplies and supply risk from Russia," ANZ Research commodity analysts said in a note. Political tension has mounted as Russia has amassed troops on the border of Ukraine.

Analysts pointed to OPEC supply additions running below their allowed increase under the OPEC+ pact, as some countries, including Nigeria, are not producing their agreed volumes.

"The fundamentals remain bullish for crude again - especially if OPEC continues to struggle to hit its quota as part of the 400,000 barrels per day monthly increases, as demand strengthens," said OANDA analyst Craig Erlam.

Libya, which is exempt from OPEC supply curbs, has been hit by pipeline maintenance work and oil field disruptions. However on Monday, production resumed at the El Feel oil field, where an armed group halted output last month.

The market is waiting on U.S. oil and product inventory data from the American Petroleum Institute (API), an industry group, due at 2130 GMT on Tuesday, followed by data from the U.S. Energy Information Administration on Wednesday.

Six analysts polled by Reuters expect U.S. crude stockpiles fell by about 2 million barrels in the week to Jan. 7, which would mark a seventh straight week of declining crude inventories.