The agreement between Russian Federation and Saudi Arabia - two of the world's biggest oil producers - helped strengthen relations between the two countries, which previously had a relatively frosty relationship.
Brent crude futures gained 2 cents to $62.31 a barrel at 12:17 p.m. EDT (1617 GMT).
In terms of oil prices, EIA said Brent crude oil spot prices averaged 71 US dollars per barrel in May, largely unchanged from April 2019 and nearly 6 dollars per barrel lower than the price in May of previous year.
China's crude oil imports slipped to around 40.23 million tonnes in May, from an all-time high of 43.73 million tonnes in April, customs data showed, due to a drop in Iranian imports caused by US sanctions and refinery maintenance.
Stock markets rose on Monday after a deal between the United States and Mexico to combat illegal migration from Central America late last week removed the threat of USA tariffs on goods imported from Mexico.
Barclays bank, in a note, said its economists had revised down their GDP growth outlook for the United States, China, India and Brazil - countries that account for more than three-quarters of their oil demand growth assumptions for this year.More news: Lasith Malinga to leave the team after Bangladesh match
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Russia's average oil output stood at 11.04 million barrels per day (bpd) on June 1-10, up from an average of 10.87 million bpd on June 1-3, two sources familiar with official data said on Tuesday.
All eyes will be on the upcoming The Organization of the Petroleum Exporting Countries (OPEC) meeting during June 25-26, when it decides its output policy for the rest of the year. The deal is due to expire this month.
Russian Federation is the only major oil producer which has not yet signed up to an OPEC agreement on global output, Saudi Arabia's Energy Minister Khalid al-Falih said on Monday.
Front-month Brent crude futures, the global benchmark for oil prices, were at $62.36 at 0023 GMT, 7 cents, or 0.1%, above Friday's close.
Nonetheless, "even planned and unintentional supply restrictions of more than 4 million barrels per day (bpd) have not been able to support prices as economic considerations took over in the last two weeks", he added.
Traders said crude prices were rising because of statements by OPEC's biggest producer Saudi Arabia on Friday saying that the group was close to agreeing extending supply cuts.