The end of the USA sanction waivers for all Iranian all buyers means that Iran's oil exports will drop as of this month, but no one is really sure by how much.
US West Texas Intermediate (WTI) crude futures were up 13 cents at $61.83, having earlier hit $62.49.
The United States escalated its tariff war with China on Friday by increasing levies to 25% for $200 billion worth of Chinese goods. The comments dragged on both Asian and USA stock markets.
To make OPEC's task even more hard, Russia halted last month supplies via the Druzhba oil pipeline to several European countries due to a contamination issue, which the Russians say was deliberate.
"The spat has reinvigorated demand-side concerns, given that the conflict has been adversely impacting prospects for global economic growth".
The United States reimposed sanctions on Iran in November after pulling out of a 2015 nuclear accord between Tehran and six world powers past year, though it allowed Tehran's biggest buyers to continue purchasing oil via waivers for another six months.
"The threat of military action with Iran appears to have heightened".
Nigeria boosted its crude oil production in April to a 14-month high of 1.95 million barrels per day despite the supply cuts led by the Organisation of Petroleum Exporting Countries, according to an S&P Global Platts survey.
Saudi Arabia plans to meet all requests for oil purchases it has received for June, notably from countries that had to stop buying Iranian crude because of recent USA sanctions.
Bank of America Merrill Lynch said it expected Saudi Arabia "to bring back oil production slowly as Iranian barrels exit the market", adding that it expects Brent to have a floor at $70 a barrel in current market conditions.
Oil Minister Dharmendra Pradhan had said "a robust plan for an adequate supply of crude oil to Indian refineries" is in place.
Prices were supported by tighter supply amid continuing production cuts by the Organisation of the Petroleum Exporting Countries (OPEC) and USA sanctions on Iran and Venezuela.
The kingdom will continue to export less than 7 million barrels a day in June, the person said. The latest forecast puts the United States on track to reach the 13-million-bpd milestone in the fourth quarter of 2019.
India was the second biggest buyer of Iranian crude oil after China. State media did not immediately report the incident.