Brent crude futures were up 3 cents at $62.17 a barrel by 0330 GMT.
After last week tankers attacks the tension in the Middle East remain high, with Trump saying he prepared to take military action to prevent Iran having a nuclear bomb but left open whether he would sanction the use of force just to protect Gulf oil supplies.
Iran said it shot down an American drone that was spying and stated it would "defend Iran's airspace and maritime boundaries with all our might".
The drone was downed in global airspace over the Strait of Hormuz by an Iranian surface-to-air missile, a USA official said on Thursday, speaking on condition of anonymity.
OPEC with Russian Federation and other non-OPEC producers are now set to decide whether OPEC+ extends or adjusts the supply deal that involves cutting 1.2 million bpd.
It said an OPEC committee sees global oil inventories shrinking by nearly 500,000 barrels a day if the group keeps restraining supplies.
In its latest Short-Term Energy Outlook (STEO) released last week, EIA forecast annual US crude oil production will increase by 1.4 million b/d in 2019 and by 0.9 million b/d in 2020, with 2020 production averaging 13.3 million b/d.
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Whilst tensions in the middle east have caused the spike in oil prices today and earlier in the month, there are several other factors supporting oil.
After swelling to near two-year highs, USA crude stocks fell by 3.1 million barrels last week, compared with analyst expectations for a draw of 1.1 million barrels, the Energy Information Administration (EIA) said on Wednesday.
Oil prices extended gains on Wednesday after rising in the previous session on rekindled hopes for a U.S.
After weeks of swelling, USA crude stocks fell by 812,000 barrels last week to 482 million, the American Petroleum Institute said on Tuesday, a smaller fall than the 1.1-million-barrel drop analysts had expected. Washington and Riyadh have blamed Tehran for the attacks, which Iran has denied.
That and the bullish EIA report "all begin to reduce the uncertainties for an oil market that has a whole bunch of them, maybe the biggest of which is where demand is going to go", said Rob Thummel, managing director at Tortoise, a Kansas-based money manager that oversees $21 billion in assets.
The New York Federal Reserve said on Monday that its gauge of business growth in New York State posted a record fall this month to its weakest level in more than 2 to 1/2 years, suggesting an abrupt contraction in regional activity. "A positive outcome with the US - China would be icing on the cake", said Edward Moya, senior market analyst at brokers OANDA.