Investors also weighed OPEC-led efforts to tighten crude supply against the restart of Libya's biggest oilfield and the prospect of weaker demand from China.
Brent, the international benchmark, settled at $65.86 a barrel, up 19 cents. U.S. West Texas Intermediate crude settled at $56.56 a barrel, down 3 cents.
"Oil is still waiting for a deal to come back to table with China," said Phillip Streible, senior commodities strategist at RJO Futures.
U.S. Secretary of State Mike Pompeo said President Donald Trump would reject any trade deal that is not perfect, but added the White House would keep working on an agreement.
"Things are in a good place, but it's got to be right," Pompeo told Sinclair Broadcasting Group.
Supply curbs by the Organization of the Petroleum Exporting Countries and allies helped support crude. On Monday, Russia said it would speed up output cuts this month, and OPEC sources this week also said the group would likely extend its output cut pact that has driven oil prices about 20 percent higher this year.
"By them kicking the can down the road, and not making a decision on production until June, the die has basically been cast for the start of U.S. summer driving season. You'd think that'd be pretty bullish," said Phil Flynn, analyst at Price Futures Group in Chicago.
The restart of Libya's El Sharara oilfield could offset some of the cuts, however. The field, with a capacity of 315,000 barrels a day, had been closed since December.
The market expects U.S. inventory reports will show rising crude stockpiles. Analysts polled by Reuters estimated, on average, that crude stocks rose 1.2 million barrels in the week to March 1. [EIA/S]
The first supply report is due at 4:30 p.m. EST (2130 GMT)from the American Petroleum Institute (API), an industry group, followed by the government's official figures on Wednesday. [API/S]
Concern about an economic slowdown in China weighed on prices.
China's government said it is targeting economic growth of 6.0 to 6.5 percent in 2019, lower than the 6.6 percent growth reported last year and raising the prospect of slowing fuel demand.
"China's downward revision in their expected GDP gains for this year conjured up further ideas of smaller-than-expected oil demand increases in the coming months," Jim Ritterbusch, president of Ritterbusch and Associates, said in a note. - Reuters
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