UPDATE 7-Oil rallies as stock market rebounds

* Stock market rebound boosts oil prices

* Conflict in Syria keeps markets on edge

* Trade dispute between U.S., China unsettles market

* Graphic on U.S. vs China tariffs: https://tmsnrt.rs/2GXE9qr (Updates prices, market activity, adds commentary; changes byline, dateline to NEW YORK, previous LONDON)

NEW YORK, April 9 (Reuters) - Oil prices rose on Monday, supported by a rebound in the stock market as concerns of a trade war between the United States and China eased.

Brent crude futures rose $1.25 to $68.36 a barrel, a 1.9 percent gain, by 12:29 p.m. EDT (1629 GMT).

U.S. West Texas Intermediate (WTI) crude futures rose $1.21 to $63.27 a barrel, a 2.0 percent gain.

Prices were on track for their largest daily percentage gain since March 23.

"Once again we find the oil market being swept up in broader market sentiment," said Matt Smith, director of commodity research at ClipperData. "After Friday's flight from risk, the positive mood in equities to start the week is encouraging a rebound in oil, with a weakening dollar providing a further shot in the arm."

The U.S. stock market broadly rose more than 1 percent. Crude futures have recently tracked with equities.

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

Market participants also focused on an air strike on a Syrian air base over the weekend. Syria and its main ally Russia blamed Israel for carrying out an attack on a Syrian air base near Homs on Monday which followed reports of a poison gas attack by President Bashar al-Assad's forces on a rebel-held town.

The Pentagon formally denied a Syrian state television report that the U.S. military had fired missiles at a Syrian government air base.

Prices have been supported so far this year by healthy demand and supply restraint led by the Organization of the Petroleum Exporting Countries, which started in 2017 to rein in oversupply and prop up prices.

"From a pure short-term fundamental perspective, odds still tilt bullish in our view," Jim Ritterbusch, president of Ritterbusch and Associates, said in a note.

In physical oil markets, OPEC's No. 2 producer Iraq said on Monday that it will keep prices steady for its May crude supplies.

WTI's discount to Brent recently has widened to its largest since January, reflecting some of the investor caution over rapidly expanding U.S. output <WTCLc1-LCOc1>.

However, production from the prolific Permian basin may already be outpacing pipeline takeaway capacity and could prompt producers to slow down drilling.

(Additional reporting by Amanda Cooper in London and Henning Gloystein in Singapore; Editing by Tom Brown)