The end of the US 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 $0.43 at $62.13, having earlier hit $62.49.
Both Sinopec and CNPC declined to comment.
Brent oil dropped below $70 a barrel on Wednesday, hurt by concerns about a deepening US-Chinese trade row, although persistent supply worries prevented a steeper price fall.
"The spat has reinvigorated demand-side concerns, given that the conflict has been adversely impacting prospects for global economic growth".
Last month, Washington said it will end Iran sanction waivers that have been granted to China, India, Greece, Italy, Taiwan, Japan, Turkey and South Korea to ensure low oil prices and avoid disruption to the global oil market.
United States officials announced on Sunday that the movement of an aircraft carrier strike group and a bomber task force towards the Middle East was meant to counter "credible threats", but Tehran dismissed the move as "psychological warfare". During the latest fiscal year ending March 31, Iran was India's third-largest oil supplier behind Iraq and Saudi Arabia.
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Background: Ahead of the expiration of USA sanction waivers in May, India's imports of Iranian oil fell to 304,500 bpd last month - a 45 percent dropoff from 552,000 bpd in April 2018.
US Energy Secretary Rick Perry said on Tuesday that Saudi Arabia was increasing its oil production to meet needs arising from sanctions on Iran.
Washington has also placed sanctions on oil exports from Venezuela, a founding member of the Organisation of the Petroleum Exporting Countries (Opec).
Although OPEC and 10 non-OPEC partners had in December, agreed on a new supply accord, which runs from January-June, which exempts Iran, Libya, and Venezuela, Nigeria's output has been on the rise since the beginning of the year.
The kingdom will continue to export less than 7 million barrels a day in June, the person said.
The EIA forecast output in 2020 will rise by 930,000 bpd to 13.38 million bpd, a bigger increase than it previously estimated.
CNPC, whose Iranian oil comes mostly from its investments at two Iranian oil fields, is also skipping imports for this month, said one of those sources.