* U.S. drillers cut rigs for first time in three weeks
* Concerns of U.S. sanctions against Iran also support crude
* Rising Russian output, U.S-China trade spat limit gains (Updates prices, changes dateline, adds analyst quote paras 5-6)
LONDON, April 2 (Reuters) - Oil rose towards $70 a barrel on Monday, lifted by a drop in drilling activity in the United States and concerns that Washington could reintroduce sanctions against Iran.
U.S. drillers cut seven oil rigs in the week to March 29, bringing the total down to 797, the first decline in three weeks. The rig count is closely watched as an indicator of future U.S. oil output.
Brent crude, the international benchmark, rose 58 cents to $69.92 a barrel at 0850 GMT. It was still below its 2018 high of $71.28 reached on Jan. 25. U.S. crude added 38 cents to $65.32.
Trading volume was lower than normal as many countries were still on Easter holiday.
"The market is set for a re-test of the highs of 2018," said Olivier Jakob, oil analyst at Petromatrix.
"The Iranian factor is going to be a very significant input for the next four weeks. It is going to be an underlying support for the whole month."
U.S. President Donald Trump has threatened to pull out of a 2015 international nuclear deal with Tehran under which Iranian oil exports have risen. He has given the European signatories a May 12 deadline to "fix the terrible flaws" of the deal.
Oil has risen from a multi-year low near $27 in January 2016, helped by production cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia, which started in 2017 and is due to run until the end of 2018.
The revival in prices has helped to support a surge in U.S. drilling, which has boosted U.S. production to a record 10.43 million barrels per day (bpd), taking it past top exporter Saudi Arabia.
Russian oil output rose in March despite the output deal, to 10.97 million bpd from 10.95 million bpd in February, Russian Energy Ministry data showed, putting Russia ahead of the United States as the world's biggest crude producer.
Also potentially weighing on markets were rising trade tensions between the United States and China.
China increased tariffs by up to 25 percent on 128 U.S. products from Monday, escalating a spat between the world's biggest economies in response to U.S. duties on imports of aluminum and steel.
"Investors took their cue from falling U.S drilling counts," said Wang Xiao of Guotai Junan Futures. "But increasing trade friction between China and the U.S. is likely to rock global markets and tarnish bullish sentiment in crude oil markets."
(Additional reporting by Meng Meng in BEIJING and Henning Gloystein in SINGAPORE; Editing by Susan Fenton)