* 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 throughout, adds comment, changes dateline from SINGAPORE)
LONDON, March 26 (Reuters) - Crude oil futures slipped on Monday, but losses were capped by a rebound in stock markets and escalating Saudi-Iran tensions.
Global stocks came off six-week lows on optimism that the United States and China are set to begin trade talks, easing fears about a trade war between the world's two largest economies.
The possibility of a full-blown trade war had weighed on the energy complex on fears that it could harm oil demand.
Brent crude futures were down 10 cents at $70.35 a barrel at 1000 GMT. U.S. West Texas Intermediate (WTI) crude futures fell 26 cents to $65.62.
U.S. President Donald Trump last week signed a memorandum that could impose tariffs on up to $60 billion of imports from China.
"The ... trade war story ... should be taken into account when trying to quantify the potentially bullish effect of the geopolitical element in oil markets," said analysts at consultancy JBC Energy.
The market also found support from rising Middle East tensions.
Saudi air defences shot down seven ballistic missiles fired by Yemen's Iran-aligned Houthi militia on Sunday, some of which targeted Saudi capital Riyadh.
"Geopolitics and growing concerns about the United States leaving the Iran deal lifted oil prices back towards $70 per barrel," said Norbert Rucker, head of macro and commodity research at private Swiss bank Julius Baer.
Beyond trade concerns, crude was pressured by a rise in the number of active U.S. oil rigs to a three-year high of 804, implying further rises in production. <C-OUT-T-EIA> U.S. oil output has already jumped by a quarter since mid-2016 to 10.4 million barrels per day (bpd).
"With US crude production likely to be close to 10.5 million bpd 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 said
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. ($1 = 6.3080 Chinese yuan renminbi)
(Additional reporting by Henning Gloystein in Singapore Editing by David Goodman)