* U.S. crude inventories rise more than expected last week -EIA
* U.S. gasoline, distillate stocks fall for third week
* Trump says China trade talks moving along well
* Chevron, Exxon Mobil raise Permian Basin output forecasts (Updates prices, market activity and comments to settlement)
By Laila Kearney
NEW YORK, March 6 (Reuters) - Crude oil futures were mixed on Wednesday after U.S. government data showed an unexpectedly sharp build in crude inventories, though a third straight drop in gasoline stocks supported prices.
Brent crude futures settled at $65.99 a barrel, up 13 cents, or 0.2 percent. U.S. crude oil futures ended down 34 cents, or 0.6 percent, at $56.22 a barrel.
U.S. crude inventories rose 7.1 million barrels last week, far exceeding analysts' expectations for a build of 1.2 million barrels, the Energy Information Administration (EIA) said.
Gasoline stocks, however, fell 4.2 million barrels, compared with analysts' expectations for a 2.1 million-barrel drop. U.S. gasoline futures gained about 1 percent.
"A solid bearish build to crude inventories has been offset by some chunky draws to the products," said Matthew Smith, director of commodity research at ClipperData.
Crude futures also tracked a slump in U.S. equities, which sputtered without positive developments in trade talks between Washington and Beijing.
U.S. President Donald Trump said trade talks were moving along well, but offered few details.
"Selling in equities played a significant part in today’s oil price weakness," Jim Ritterbusch, president of Ritterbusch and Associates, said in a note. "Further reduction in risk appetite and any additional downgrades in the global economic growth path could eventually weigh across the energy spectrum."
The markets have been hit by surging U.S. crude production, which, according to the EIA, held at an all-time high of 12.1 million barrels per day last week.
The rise in North American production undermines supply cuts led by the Organization of the Petroleum Exporting Countries and its non-member allies, including Russia, that has helped crude prices rise about 20 percent this year.
OPEC and its partners have pledged to curb output by 1.2 million bpd, and they are likely to push back their decision whether to extend the production agreement to June from April, sources said.
Chevron Corp and Exxon Mobil Corp released rival Permian Basin projections on Tuesday pointing to increased shale oil production in the largest U.S. oil patch.
The increases would cement the pair as the dominant players in the West Texas and New Mexico field, with one-third of Permian production potentially under their control within five years. (Additional reporting by Stephanie Kelly in New York, Koustav Samanta in SINGAPORE, Dmitry Zhdannikov in London; editing by Marguerita Choy and Richard Chang)