* Trump threatens China with tariffs on further goods
* U.S. crude oil output hits record 12.4 million bpd - EIA
* Putin says Russia, Saudi Arabia differ on fair price
* GRAPHIC-Oil moves into bear market: https://tmsnrt.rs/2WICWvf
* GRAPHIC-Crude output, storage surge: https://tmsnrt.rs/2DwTUBQ (Updates prices, market activity and comments)
NEW YORK, June 6 (Reuters) - Oil prices were little changed on Thursday, after falling to near five-month lows in the previous session, as sentiment remained dim on fresh signs of a stalling global economy and ongoing concerns about U.S. crude supply growth.
Brent crude futures were up 4 cents to $60.67 a barrel by 1:27 p.m. EDT (1727 GMT), while U.S. West Texas Intermediate crude futures lost 6 cents to $51.62 a barrel.
On Wednesday, the two benchmarks hit their lowest levels since mid-January at $59.45 and $50.60, respectively, after U.S. crude production hit a new record high and stockpiles hit their highest since July 2017.
Both Brent and U.S. crude are in bear-market territory, having lost more than 20% from peaks reached in late April.
"While much attention has been paid to a rising and record pace of U.S. crude production in contributing to the strong crude supply hike ... it is becoming increasingly apparent to us that a softening in demand has also been a major contributor," Jim Ritterbusch, president of Ritterbusch and Associates, said in a note.
Signals of slowing global economic activity have increased in recent months, fueled by trade tensions between the United States and China, the world's top two energy consumers.
"Worries about demand destruction are really driving prices lower," said Gene McGillian, vice president of market research at Tradition Energy.
U.S. President Donald Trump, in his latest public comments about the trade war, said he would likely decide on more China tariffs at the end of June, which followed his overnight threat to put tariffs on "at least" another $300 billion worth of Chinese goods.
The European Central Bank's decision to push back the timing of its first post-crisis interest rate hike also weakened the global economic outlook and cooled expectations for crude demand.
Prices rallied strongly in the first five months of the year to a high of nearly $75 a barrel, supported by supply curbs by the Organization of the Petroleum Exporting Countries and some allies including Russia. Supply has also been limited by U.S. sanctions on oil exports from Iran and Venezuela.
Members of the OPEC+ group are set to discuss whether to extend their supply curbs further later this month.
President Vladimir Putin said on Thursday that Russia had differences with OPEC over what constituted a fair price for oil but said Moscow would take a joint decision with OPEC colleagues on output at a policy meeting in the coming weeks.
U.S. crude production continues to surge, however, as increased drilling in the prolific Permian shale basin helped push output to a record 12.4 million barrels per day (bpd) by the end of May.
(Additional reporting by Ron Bousso in London, Henning Gloystein; editing by Marguerita Choy and Alexandra Hudson)