* Brent, WTI futures both up 0.3%
* Brent to hold near $63 in 2020, WTI around $57 - poll
* U.S. crude stocks fell by 7.8 mln bbls last week - API (Adds comments, updates prices)
SEOUL, Jan 2 (Reuters) - Oil prices kicked off the new year higher on Thursday as warming trade relations between the United States and China eased demand concerns, while rising tensions in the Middle East fueled worries about supply.
Global benchmark Brent crude futures, were up 22 cents, or 0.3%, to 66.22 a barrel by 0430 GMT. U.S. West Texas Intermediate (WTI) crude was up 18 cents, or 0.3%, at $61.24 per barrel.
Oil markets were closed on Wednesday for New Year's Day.
Both benchmarks ended higher in 2019, posting their biggest annual gains since 2016, buoyed at the end of the year by a thaw in the prolonged trade dispute between the United States and China - the world's two largest economies - and a deeper output cut pledged by the Organization of Petroleum Exporting Countries (OPEC) and its allies.
"Oil remains supported by the back-burner trade truce and the uptick in political unrest in Iraq," said Stephen Innes, chief Asia market strategist at AxiTrader.
The U.S. military carried out air strikes against Iran-backed Katib Hezbollah militia group over the weekend. Angry at the air strikes, protesters stormed the U.S. Embassy in Baghdad on Wednesday, although they withdrew after the United States deployed extra troops.
In 2020, Brent is forecast to average $63.07 a barrel, up from December's estimate of $62.50, while WTI is forecast to average $57.70 a barrel, up from December's estimate of $57.30, as the OPEC-led supply cuts and the expectations of a U.S.-China trade deal boosted analysts' views on the prospects for the year, a Reuters poll showed.
U.S. President Donald Trump said on Tuesday the U.S.-China Phase 1 trade deal would be signed on Jan. 15 at the White House.
January also marks the start of the deeper output cuts by OPEC and its partners, including Russia. OPEC and its allies have agreed to cut a further of 500,000 barrels per day (bpd) from Jan. 1, on top of their previous cut of 1.2 million bpd that started on Jan. 1 a year ago.
A fall in U.S. crude inventories last week also supported prices. U.S. crude stocks fell 7.8 million barrels in the week ended Dec. 27, compared with analysts' expectations for a decrease of 3.2 million barrels, according to data from the American Petroleum Institute (API) released on Tuesday.
Official data from the Energy Information Administration (EIA) is due on Friday as the release has been delayed by two days by the New Year's holiday.
"Traders will look towards Friday's EIA report for forward guidance on oil prices," said Benjamin Lu, analyst at Singapore-based brokerage Phillip Futures. (Reporting By Jane Chung; Editing by Tom Hogue and Himani Sarkar)