UPDATE 2-Oil prices firm, but trade dispute and Syria keep market on edge

* Trade dispute between U.S./China unsettles markets

* Conflict in Syria also keeps markets on edge

* U.S. drillers add 11 rigs drilling for new oil

* Graphic on U.S. vs China tariffs: https://tmsnrt.rs/2GXE9qr (Adds Syria conflict, comment, updates prices)

SINGAPORE, April 9 (Reuters) - Oil markets stabilized on Monday after slumping around 2 percent last Friday on concerns over an intensifying trade dispute between the United States and China, as well as increased U.S. drilling activity.

Markets on Monday were also eyeing the situation in Syria after reports - denied by the Pentagon - that U.S. forces had struck a major air base there.

U.S. WTI crude futures were at $62.34 a barrel at 0355 GMT, up 28 cents, or 0.45 percent, from their previous settlement.

Brent crude futures were at $67.43 per barrel, up 32 cents, or 0.5 percent.

Oil prices fell about 2 percent on Friday after U.S. President Donald Trump threatened new tariffs on China, reigniting fears of a trade war between the world's two largest economies that could hurt global growth.

With Chinese markets closed last Thursday and Friday, Shanghai crude futures played catch-up on Monday, dropping 0.6 percent to around 400 yuan ($63.43) per barrel.

"Oil prices have been susceptible to the brewing trade tensions between China and the U.S....However, fundamental support levels have been demonstrated with OPEC's suggestion on an production limit extension into 2019," said Singapore-based Phillip Futures.

Oil prices have generally been supported by healthy demand as well as by supply restraint led by the Organization of the Petroleum Exporting Countries (OPEC), which started in 2017 in order to rein in oversupply and prop up prices.

In physical oil markets, OPEC's number two producer Iraq said on Monday that it is keeping prices for its crude supplies in May steady.

In the United States, drillers added 11 rigs looking for new production in the week to April 6, bringing the total count to 808, the highest level since March 2015, General Electric's Baker Hughes energy services firm said on Friday.

As a result, U.S. exports have soared in recent months, "more than offsetting the Venezuelan supply disruption" as a result of the economic crisis in the South American OPEC-member, Innes said. ($1 = 6.3059 Chinese yuan renminbi)

(Reporting by Henning Gloystein; editing by Richard Pullin)