* Dollar rallies after Fed starts to cut bond buying
* Weekly U.S. crude stocks down 2.94 mln barrels
* Brent underpinned by continued Libyan outages
(Recasts, updates prices, adds fresh quotes, previous SINGAPORE)
LONDON, Dec 19 (Reuters) - Brent crude oil futures held steady at over $109 a barrel on Thursday as the market shrugged off a move by the U.S. Federal Reserve to reduce its monetary stimulus programme, and remained focused on U.S. crude stock draws.
Brent crude was down 17 cents to $109.46 a barrel by 0922 GMT, after ending $1.19 higher on Wednesday. U.S. oil fell 3 cents to $97.77, after ending 58 cents up.
Oil prices faced some headwinds early in the session after the dollar rallied hard on the Federal Reserve's decision to reduce its bond buying, but this was the full extent of the impact.
"The 'tapering proclamation' yesterday gained a lot of attention - but it also turned out to be a non-event - oil price-wise," said Michael Poulsen, oil risk manager at Global Risk Management.
The dollar index was up 0.59 percent against a basket of currencies at 0917 GMT. A stronger dollar is negative for oil as it makes the commodity more expensive for holders of other currencies.
Aside from this, analysts said the oil market was unaffected. "We're not seeing much of a reaction," said Ole Hansen, senior commodity strategist at Saxo Bank.
"Those who want to sell on the back of less liquidity will be met by those who want to buy as this is an indication that the Fed now believes the growth outlook is improving and that is what really drives these cyclical commodities."
Traders have had plenty of time to prepare for the Fed's move as the economic data coming out of the United States has been generally positive over the last few months. The decision was also tempered by the Fed's suggestion that its key interest rate would stay near zero even longer than previously promised.
The Fed's move came in the wake of Wednesday's U.S. oil inventories report showing stock draws for a third week in a row, and a big, unexpected fall in distillates stocks. This leant support to crude prices.
Analysts at BNP Paribas said that the 2.9 million barrel draw in U.S. crude stocks had been driven by higher refinery demand, as plants are ramping up following the completion of seasonal maintenance.
Over the last three weeks, stocks have fallen by 18 million barrels. "Refinery operators are taking advantage of superior refining margins that are being driven by relatively cheap cost of inputs," the analysts said in a note.
Brent also remains elevated at just under $110 because of continued Libyan outages. A mix of militias, tribesmen and civil servants demanding political rights or a greater share of Libya's oil wealth have occupied several oilfields and ports, bringing down exports to 110,000 barrels per day (bpd) from more than 1 million bpd in July.
With the Fed's announcement out of the way, and traders closing their books ahead of the Christmas holidays, oil prices are expected to remain range-bound for the rest of the year, barring surprises.
"It will take quite a bit of news to push these markets now - this was really the last event this year," said Hansen, who expects to see U.S. crude trading at around $95.50-$99 a barrel, and Brent around $106-$111 a barrel until year-end.
(Additional reporting by Manash Goswami in Singapore; editing by Keiron Henderson)