Tensions in the Middle East after last week's tanker attacks also lent support.
Brent crude futures were trading 93 cents higher at $61.87 a barrel by 1403 GMT, after hitting a session low of $60.25. U.S. West Texas Intermediate crude futures gained $1.37 to $53.30, off a session low of $51.50.
"Had a very good telephone conversation with President Xi of China.
We will be having an extended meeting next week at the G-20 in Japan. Our respective teams will begin talks prior to our meeting," Trump tweeted on Tuesday.
Fears of a confrontation between Iran and the United States have mounted since last Thursday's oil tanker attacks, which Washington has blamed on Tehran. Iran has denied involvement.
Iran on Monday said it would breach internationally agreed curbs on its stock of low-enriched uranium within 10 days, adding that European nations still had time to save a landmark nuclear deal.
Acting U.S. Defense Secretary Patrick Shanahan announced on Monday the deployment of about 1,000 more troops to the Middle East for what he said were defensive purposes, citing concerns about a threat from Iran.
Saudi Arabian Energy Minister Khalid al-Falih said on Monday that countries need to cooperate on keeping shipping lanes open for oil and other energy supplies.
He also said that Saudi exports and production are expected to remain at "about the same level" as the past few months.
Market participants are also awaiting a meeting between the Organization of the Petroleum Exporting Countries and other producers including Russia, a group known as OPEC+, to decide whether to extend a supply reduction pact that ends this month.
Russian Energy Minister Alexander Novak said on Tuesday it was too early to make any decisions about the future of the agreement because of market uncertainties.
Oil prices have fallen by about 20pc from April's 2019 highs, partly because of concerns over the U.S.-China trade war and disappointing economic data.
The New York Federal Reserve said on Monday its gauge of business growth in New York state posted a record fall this month to its weakest level in more than 2-1/2 years, suggesting an abrupt contraction in regional activity.