Brent crude slipped 14 cents to $66.36 a barrel, after earlier hitting $66.65, close to its 2019 high of $66.83 reached on Monday. U.S. crude settled up 50 cents at $56.09 a barrel, maintaining its high for the year.
"I think the market is looking for an excuse to follow through on the breakout, but there are still a lot of questions surrounding the U.S.-China trade deal" and the global economy, said Phil Flynn, an analyst at Price Futures Group in Chicago.
A fresh round of talks aimed at resolving the trade dispute between the United States and China were scheduled to start on Tuesday in Washington, with higher-level discussions planned for later in the week.
Traders said they were cautious about taking large new positions before the outcome of the talks.
In a warning sign about the economic outlook, Europe's biggest bank HSBC warned it may delay some investments this year as it missed 2018 profit forecasts due to slowing growth in China and Britain.
The Organization of the Petroleum Exporting Countries last week lowered its forecast for growth in world oil demand in 2019 to 1.24 million barrels per day and some analysts believe it could be weaker still.
"Given a continuously uncertain economic picture, our already relatively bearish outlook for 2019 of below 1 million bpd in global oil demand growth may be subject to further downwards revisions," analysts at JBC Energy wrote.
To stop a build-up of inventories that could weigh on prices, the group of OPEC and allies like Russia, known as OPEC+, began a new supply cut of 1.2 million bpd on Jan. 1. The cuts have helped crude to rise more than 20 percent this year.
In keeping with that aim, Russian President Vladimir Putin and King Salman bin Abdulaziz Al Saud of Saudi Arabia, OPEC's de facto leader, said they supported continued coordination on the global energy markets, the Kremlin said on Tuesday.
The statement eased some doubts that Russia would stick to the pact, investors said.
U.S. sanctions against exporters Iran and Venezuela have provided additional support to the market.
Venezuela is a major crude supplier to U.S. refineries. Iran's exports, while down steeply since the sanctions began in November, have risen in early 2019, according to tanker data and sources.