* U.S. softens stance on Huawei buying tech components
* Trump says not ready to make a trade deal with China OPEC sees bearish oil market for rest of 2019
* POLL-U.S. crude stocks fell last week, products seen rising
* Coming Up: API's U.S. oil inventory report at 4:30 p.m./2030 GMT (Adds settlement prices, latest Trump comments on trade deal)
By Jessica Resnick-Ault
NEW YORK, Aug 20 (Reuters) - Oil prices steadied on Tuesday on optimism U.S.-China trade tensions will ease and hopes major economies will take stimulus measures to ward off a possible economic slowdown, after falling earlier on concerns over future demand.
Brent crude settled 29 cents, or 0.5%, higher at $60.03 a barrel, while U.S. crude rose 13 cents to $56.34 a barrel. U.S. crude turned lower in post-settlement trade after U.S. President Donald Trump said he was not ready to make a trade deal with China.
The United States said it would extend a reprieve that permits China's Huawei Technologies to buy components from U.S. companies, signalling a slight softening of the trade conflict between the world's two largest economies.
"It's the ebbing and flowing of the U.S.-China trade war and some hope of economic stimulus that's coming at these markets, including potential fiscal stimulus by the Germans," said John Kilduff, a partner at Again Capital in New York.
Concerns over the overall level of demand for oil continue to weigh on crude prices. The Organization of the Petroleum Exporting Countries cut its forecast for global oil demand growth in 2019 by 40,000 barrels per day (bpd) to 1.10 million bpd and indicated the market would be in slight surplus in 2020.
A rally in equity markets around the world on growing expectations that global economies will take action against slowing growth also gave oil prices a floor.
China's new lending reference rate was set slightly lower on Tuesday after the central bank announced interest rate reforms designed to reduce corporate borrowing costs, while in Germany there were also positive moves.
Germany's coalition government said it would be prepared to ditch its balanced budget rule and take on new debt to counter a possible recession.
"China's announcement of key interest rate reforms over the weekend has driven expectations of an imminent reduction in corporate borrowing costs," Cantor Fitzgerald said in a note.
Traders were also watching for signs of tension in the Middle East after the United States described as unfortunate the release of an Iranian tanker at the centre of a confrontation between Iran and Washington, warning Greece and Mediterranean ports against helping the vessel.
Also, the market awaits weekly data on U.S. inventories, which was expected to show a 1.9 million-barrel drop in crude stocks for last week. The American Petroleum Institute (API), an industry group, reports its estimates at 4:30 p.m., followed by and government data on Wednesday morning.
Additional reporting by Jessica Jaganathan in Singapore Editing by Marguerita Choy and David Holmes