Brent oil rose slightly on Tuesday supported by demand for U.S. heating oil and gasoline, which gained on expectations that persistent cold weather in the United States will lead to another large draw in distillates.

Frigid weather supported heating oil prices and U.S. RBOB futures saw some strength from traders unwinding the spread trade between the heating fuel and gasoline, one trader said.

Oil markets had a muted reaction to U.S. Federal Reserve Chair Janet Yellen's remarks that she will not make any abrupt changes in the U.S. central bank's monetary policy, and that the Fed will continue to reduce its stimulus.

Instead, analysts looked to the American Petroleum Institute's weekly inventory report due out at 4:30 p.m. EST on Tuesday.

"We are seeing good demand on the product side, particularly in heating fuels, and refined products have been particularly reactive to (API) reports lately," said John Kilduff, analyst at Partner Again Capital LLC.

Brent crude settled 5 cents higher at $108.68, after settling 94 cents lower in the previous session.

U.S. crude rose earlier in the session supported by the strong equities markets, but ended the day 12 cents lower at $99.94.

U.S. ultra-low sulfur diesel (ULSD) settled 3 cents higher at $3.0281 per gallon. Gasoline settled up 2.78 cents to $2.7526 per gallon.

U.S. crude oil prices were pressured by expectations that crude oil demand will slow as U.S. refiners enter maintenance season.

The U.S. Energy Information Administration expects U.S. oil production to drop slightly this year and next as severe winter weather cut into well completion, even as the agency expects a boost in shale oil output.

U.S. crude was still close to a six-week high, supported by expectations of a drop in distillate inventories last week due to freezing weather across the country.

Distillate stocks, including heating oil and diesel fuel, were expected to drop 2.3 million barrels along with a 100,000-barrel gasoline decline in the week to Feb. 7, according to analysts in a Reuters poll. U.S. crude oil inventories were expected to rise 2.7 million barrels.

In addition to the API data, the EIA will release its weekly inventory report to at 10:30 a.m. EST on Wednesday.

Brent's gains were capped by expectations of a further increase in Libyan output. The North African nation's current production is around 600,000 barrels per day (bpd), up from its average rate in January.

North Sea Forties crude was offered lower but buyers remained on the sidelines as traders expected differentials to weaken as European refineries enter maintenance season.

(By Elizabeth Dilts; Reporting by Jacob Gronholt-Pedersen and Alex Lawler; Editing by William Hardy, Chris Reese, Marguerita Choy and Diane Craft)