* API says U.S. crude stocks fall more than expected
* Trump says he and China's Xi will sign trade deal
* Nasdaq, S&P hit fresh highs on trade deal hopes
* OPEC+ oil output cut starts on Jan. 1 (Updates prices, market activity and comments)
NEW YORK, Dec 26 (Reuters) - Oil prices rose about 1% to the highest in more than three months on Thursday, buoyed by hopes of an end to the China-U.S. trade fight and by a report showing lower U.S. crude inventories.
Brent crude futures were up 70 cents, or 1%, to $67.90 a barrel by 1:50 p.m. EST (1850 GMT). U.S. West Texas Intermediate crude futures gained 65 cents, or 1.1%, to $61.76. Both benchmarks were their strongest since Sept. 17.
U.S. President Donald Trump said on Tuesday he and Chinese President Xi Jinping would have a signing ceremony for the so-called Phase 1 agreement to end their trade dispute that was put together earlier this month.
The prospect of a signed deal boosted Wall Street to fresh highs, helping to support crude futures, which often to follow equities.
The roughly 17-month trade war between the world's two largest economies has hit global growth and demand for oil.
Even so, Brent has still rallied 25 percent in 2019, supported by supply cuts by the Organization of the Petroleum Exporting Countries and allies including Russia.
"The stock market being strong coupled with the big drawdown that we had from the API is giving us the momentum that we have right now," said Phil Flynn, an analyst at Price Futures Group in Chicago.
Also supporting prices, the American Petroleum Institute, an oil industry group, said late on Tuesday that U.S. crude stocks fell by 7.9 million barrels last week, much more than forecast by analysts.
Trading volume remains low due to the Christmas holiday, which has delayed the release of the U.S. government's official oil inventory report by two days until Friday.
The so-called OPEC+ group agreed this month to extend and deepen production cuts that would take as much as 2.1 million barrels per day (bpd) of supply off the market from Jan. 1, or roughly 2% of global demand.
Still, U.S. producers, not party to the OPEC+ agreement, have been pumping record amounts of oil, especially shale. Growth in U.S. production is forecast by many to slow in 2020.
"Oil prices continue to show year-end strength, supported by a combination of definitive progress on the U.S.-China trade deal, the December OPEC/OPEC+ agreement and slowing shale activity," said Stephen Innes, chief Asia market strategist at AxiTrader.
But more supply is coming in the new year from OPEC members Saudi Arabia and Kuwait, which this week agreed to end a dispute over their Neutral Zone, which can supply as much as 500,000 bpd. (Additional reporting by Alex Lawler and Aaron Sheldrick; Editing Kirsten Donovan and Steve Orlofsky)