* Trade talks continuing, China says
* OPEC should make right call for fragile world economy -Birol
* U.S. crude stockpiles likely to have fallen last week -poll
* Coming Up: API's weekly U.S. oil data at 4:30 p.m. ET/2130 GMT (Updates with settlement prices)
NEW YORK, Nov 26 (Reuters) - Oil prices rose on Tuesday after news that U.S. and Chinese officials discussed trade, while predictions for a weekly draw on U.S. crude stockpiles lent some support as well.
Brent crude futures gained 62 cents to settle at $64.27 a barrel, while West Texas Intermediate crude rose 40 cents to settle at $58.41 a barrel.
The United States and China are close to agreement on the first phase of a trade deal, U.S. President Donald Trump said on Tuesday, after top negotiators from the two countries spoke by telephone and agreed to keep working on remaining issues.
In the last few months, markets have swung back and forth, rallying on headlines suggesting the barest progress, even as an agreement has yet to be nailed down.
The discussions are taking place amid heightened tensions, with China saying it had summoned the U.S. ambassador on Monday to protest against the passage in the U.S. Congress of the Hong Kong Human Rights and Democracy Act.
"The main support for prices is the idea that if we get an easing in the trade war, the fear of slowing conditions and the impact on oil and fuel demand growth will be taken out of the market," said Gene McGillian, vice president of market research at Tradition Energy in Stamford, Connecticut.
On the supply side, the Organization of the Petroleum Exporting Countries (OPEC) meets in Vienna on Dec. 5, followed by talks with the broader OPEC+ group featuring other producers that have agreed to cut output, including Russia.
The head of the International Energy Agency told Reuters that OPEC countries should make the right decision for a "very fragile" global economy.
Predicting strong oil production growth from the non-OPEC countries, especially the United States, Brazil, Norway and Guyana, Fatih Birol said: "There will be lots of oil in the markets. I hope they will make the right decision for themselves and for the global economy."
U.S. crude stockpiles were expected to have declined 400,000 barrels last week, according to a Reuters poll of analysts, ahead of reports from the American Petroleum Institute (API), an industry group, on Tuesday, and the Energy Information Administration (EIA) on Wednesday.
(Additional reporting by Bozorgmehr Sharafedin in London and Aaron Sheldrick in Tokyo; Editing by Marguerita Choy and David Goodman)