* Stocks jump amid rate-cut hopes, tech shares' bounce
* U.S. crude oil stocks unexpectedly rise 3.5 mln bbls last wk-API
* Analysts say economic slowdown starting to hit oil demand
* Russia's Rosneft seeks govt compensation for OPEC deal extension
* Downturn hits oil, LNG and coal: https://tmsnrt.rs/2WJIky2 (Adds API data and post-settlement trade)
NEW YORK, June 4 (Reuters) - Oil prices ended as much as 1% higher on Tuesday after a global stock market rally pulled Brent crude from a four-month low touched earlier in the session.
U.S. stock markets rallied almost 2% on China's request for dialog with the United States to resolve the trade dispute and comments from U.S. Federal Reserve Chairman Jerome Powell drove expectations of an interest rate cut.
Brent futures gained 69 cents, or 1.1%, to settle at $61.97 a barrel. The global benchmark fell as low as $60.21 earlier in the session, its lowest since Jan. 29.
U.S. West Texas Intermediate (WTI) crude rose 23 cents, or 0.4%, to $53.48, rising over a dollar from its session low.
Prices pared gains sharply, with WTI futures turning negative, in post-settlement trade after U.S. crude inventories unexpectedly rose 3.5 million barrels last week to 478 million, along with bigger-than-expected builds in gasoline and distillate fuels, according to data from industry group the American Petroleum Institute.
Analysts in a Reuters poll forecast a 800,000-barrel crude draw ahead of the weekly petroleum report from the U.S. Energy Information Administration (EIA) at 10:30 a.m. EDT on Wednesday.
"There is no shortage of crude oil inventories. Unless we see an across-the-board inventory drop, crude and product prices will remain under pressure," said Andrew Lipow, president of Lipow Oil Associates in Houston, noting the oil price gains on Tuesday were triggered by the stock market rally.
On Monday, Brent closed at its lowest since Jan. 28 and WTI settled at its lowest since Feb. 12.
The oil market had been weighed down earlier in the session by concerns about slowing global growth and comments from Russia's top oil producer that it would oppose extending joint cuts with the Organization of the Petroleum Exporting Countries until the end of the year.
Financial traders have been selling off energy markets on growing concerns about the outlook for the world economy amid the trade war between the United States and China and U.S. threats of tariffs on Mexican imports.
"Today's oil disconnect from the exceptionally strong equity trade appears to suggest that the oil market is more concerned about global economic growth than the stock market," Jim Ritterbusch of Ritterbusch and Associates said in a note.
Oil futures are trading around 20% below 2019 peaks reached in late April, with May posting the sharpest monthly declines since November.
Other energy prices, such as coal and gas, are also being hit hard by the economic downturn.
To prevent oversupply and prop up the market, OPEC, together with allies including Russia, has withheld supply since the start of the year.
The group plans to decide later this month or in early July whether to continue the supply curbs.
However, on Tuesday, the head of Russian state producer Rosneft, Igor Sechin, said Russia should pump at will and he would seek compensation from the government if cuts were extended.
Russia's average daily oil output, meanwhile, has dropped to a three year-low after contaminated crude clogged its main export route.
Producers are concerned that the economic slowdown will reduce fuel consumption.
Further pressuring oil prices and undermining OPEC's efforts to tighten the market has been surging U.S. output to record highs, leading to more of its crude being exported.
(Additional reporting by Scott DiSavino and Devika Krishna Kumar in New York; Henning Gloystein in Singapore and Dmitry Zhadnnikov in London; Editing by Marguerita Choy and David Evans)