* Benchmarks hit biggest annual gain in 3 years
* U.S. embassy guards in Baghdad fire stun grenades at protesters
* Oil analysts bet on modest price gains in 2020 as supply shrinks
* U.S. crude stocks fell in latest week -API (Adds API data)
NEW YORK, Dec 31 (Reuters) - Oil prices fell 1% on Tuesday, the last trading day of the decade, but notched the biggest annual gain in three years, supported by a thaw in the prolonged U.S.-China trade war and ongoing supply cuts from major oil producers.
Brent gained about 23% in 2019 and WTI rose 34%, their biggest yearly gains in three years, backed by the recent breakthrough in the trade talks and output cuts pledged by the Organization of the Petroleum Exporting Countries (OPEC) and its allies.
Forecasters do not expect oil prices to move sharply in either direction next year. Brent crude is expected to hover around $63 a barrel, a Reuters poll showed on Tuesday, down modestly from current levels, as OPEC production cuts offset weaker demand.
Over the past year, increased U.S. oil output offset the supply reductions undertaken by OPEC, led by Saudi Arabia and stemming from U.S. sanctions on Venezuela and Iran. Lackluster demand, including in developed economies, remains a primary concern headed into 2020.
"Oil prices, though largely expected to trade positive, will face headwinds from subdued global growth momentum and robust U.S. shale output levels in the first quarter (of 2020)," said Benjamin Lu, an analyst at Phillip Futures.
U.S. crude oil production in October rose to a record of 12.66 million barrels per day (bpd) from a revised 12.48 million bpd in September, the U.S. government said in a monthly report. The pace of growth is expected to slow in 2020.
Brent crude fell 67 cents, or 1%, to settle at $66.00 a barrel. U.S. West Texas Intermediate (WTI) crude fell 62 cents, or 1%, to settle at $61.06 a barrel.
On Tuesday, trade volumes were low with many market participants away for year-end holidays, amplifying the market's moves.
U.S. President Donald Trump said the Phase 1 trade deal with China would be signed on Jan. 15 at the White House. Signs of progress on the deal had boosted China's factory output and manufacturing activity in the country expanded for a second straight month.
China's Purchasing Managers' Index (PMI), which tracks economic trends in the manufacturing and service sectors, was unchanged at 50.2 in December from November, just above the 50-point mark separating growth from contraction.
Investors were nervous about the Middle East, where thousands of protesters and militia fighters gathered outside the U.S. embassy in Baghdad to condemn U.S. air strikes against Iraqi militias.
Security guards inside the U.S. embassy fired stun grenades at protesters. The U.S. ambassador and staff were evacuated due to security concerns.
"Considering that Iraq is the second-largest OPEC producer with production around 4.6 million barrels per day, market participants may add a risk premium to oil tension if tensions last for longer," UBS oil analyst Giovanni Staunovo said.
"That said, we need to see if the latest protests spread also in the south of the country, where most of the crude is exported."
On Tuesday, data from industry group the American Petroleum Institute showed U.S. crude oil stocks fell by 7.8 million barrels in the week to Dec. 27, compared with analysts' expectations for a draw of 3.2 million barrels.
(Additional reporting by Bozorgmehr Sharafedin in London and Jane Chung in Seoul, editing by David Gregorio/David Evans/Louise Heavens/Nick Macfie/Richard Chang)