* Speculators take profits
* Stock markets recover on potential U.S.-China trade talks
* U.S. rig count hits three-year high, pointing to rising output
* China launches Shanghai crude oil futures (Updates prices, adds commentary)
NEW YORK, March 26 (Reuters) - Crude oil futures slipped on Monday as investors cashed in some profits from last week's rally but concerns about Saudi-Iran tensions kept losses in check.
Brent crude futures were down 35 cents at $70.10 a barrel by 1:05 p.m. EDT (1805 GMT). U.S. West Texas Intermediate (WTI) crude futures lost 47 cents to $65.41.
Last week, Brent gained 6.4 percent and WTI rose 5.7 percent, the strongest weekly gains since July.
"I don't see anything extraordinarily bearish in the market today. I think some folks here are just ... happy to take profits," said Bob Yawger, director of energy futures at Mizuho in New York.
Although crude and product futures slipped on Monday, most share prices for energy companies, especially refiners, were up, Yawger said. The S&P Energy Index was up 0.7 percent.
Global stocks came off six-week lows on reports that the United States and China were set to begin trade talks, easing fears about a trade war. Analysts had been concerned that a trade war could hurt oil demand.
U.S. President Donald Trump last week signed a memorandum that could impose tariffs on up to $60 billion of imports from China.
"The (oil) market is pulling back after pushing strongly high last week. I think the $70 level in Brent, $67 for WTI ... start to trigger worries of increased U.S. production levels," said Gene McGillian, manager of market research at Tradition Energy in Stamford, Connecticut.
The number of active U.S. oil rigs rose to a three-year high of 804 last week, implying further rises in future production. <C-OUT-T-EIA>
"With U.S. crude production likely to be close to 10.5 million barrels per day by now and NGL (natural gas liquids) output also increasing strongly, there is a clear chance that year-on-year supply growth in the U.S. could at least temporarily hit 2 million bpd over the summer months," JBC analysts wrote.
The market found some support from rising Middle East tensions.
Saudi air defenses shot down ballistic missiles fired by Yemen's Iran-aligned Houthi militia on Sunday, some of which targeted Saudi capital Riyadh.
In Asia, Shanghai crude oil futures made a strong debut in terms of volume as investors and commodity merchants bought into the world's newest financial oil trading instrument.
Hedge funds and other money managers raised their net long U.S. crude futures and options positions in the week to March 20 after two weeks of cutting bullish bets, the U.S. Commodity Futures Trading Commission (CFTC) said on Friday.
(Additional reporting by Ahmad Ghaddar in London and Henning Gloystein in Singapore Editing by Marguerita Choy and David Gregorio)