* U.S. drillers cut rigs for first time in three weeks
* Fear of renewed U.S. sanctions against Iran also support crude
* But trade spat between U.S. and China weighs (Adds Shanghai prices and quote)
SINGAPORE/BEIJING, April 2 (Reuters) - Oil prices rose on Monday, lifted by a drop in U.S. drilling activity as well as by expectations that the United States could re-introduce sanctions against Iran.
U.S. WTI crude futures were at $65.21 barrel at 0122 GMT, up 27 cents, or 0.4 percent, from their previous settlement.
Brent crude futures were fetching $69.71 per barrel, up 37 cents, or 0.55 percent.
Shanghai September crude futures were at 415.6 yuan ($66.26) per barrel, up 0.9 percent.
Stephen Innes, head of trading for Asia/Pacific at futures brokerage OANDA in Singapore, said oil markets remained nervous about "whether or not the U.S. administration will scrap or maintain the fragile nuclear deal with Iran."
Innes said prices were also supported by a weekly report that there was a drop in activity of drilling for new oil production in the United States.
U.S. drillers cut seven oil rigs in the week to March 29, bringing the total count down to 797 <RIG-OL-USA-BHI>, General Electric Co's Baker Hughes energy services firm said in its closely followed report last Thursday. It was the first time in three weeks that the rig-count fell.
Baker Hughes published its North American rig count report on Thursday, one day earlier than usual, due to the Good Friday holiday on March 30.
Oil prices have generally been supported by supply restraint led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia, which started in 2017 in order to rein in oversupply and prop up prices.
Rising trade tensions between the U.S. and China are likely to weigh on sentiment and could make for volatile trading in the coming days, traders and analysts said.
China slapped extra tariffs of up to 25 percent on 128 U.S. products including frozen pork, as well as wine and certain fruits and nuts, in response to U.S. duties on imports of aluminum and steel, the country's finance ministry said on Sunday night.
"Investors took their cue from falling U.S drilling counts," Wang Xiao, head of crude oil research with Guotai Junan Futures said. "But increasing trade friction between China and U.S. is likely to rock global markets and tarnish bullish sentiment in crude oil markets."
Trading volumes on Monday are likely to be low as many countries, especially in Europe, will still be on Easter holiday.
($1 6.2726 Chinese yuan renminbi)
(Reporting by Henning Gloystein in SINGAPORE and Meng Meng in BEIJING Editing by Aaron Sheldrick)