Iran said on Friday it could "easily" hit US warships in the Gulf, the latest in days of sabre-rattling between Washington and Tehran, while its top diplomat worked to counter US sanctions and salvage a nuclear deal denounced by President Donald Trump.
US sanctions on Iran have already cut the OPEC member's crude exports further in May, adding to supply curbs implemented through an OPEC-led pact for the first six months of the year.
Brent crude was up 5 cents at $72.67 a barrel by 11:21 a.m. EDT (1521 GMT).
The global benchmark was set to rise nearly 3 percent this week, having ended last week largely steady and fallen the week before.
US West Texas Intermediate crude added 48 cents to $63.35, and was on track for a weekly gain of about 2.7 percent.
"Despite what we view as a balanced oil market both domestically and globally, oil pricing is apparently still sensitive to evolving developments in the Persian Gulf where occasional minor military events are slowly cranking up geopolitical risk premium," said Jim Ritterbusch, president of Ritterbusch and Associates.
Iran's foreign ministry on Friday rejected accusations by Saudi Arabia that Tehran had ordered an attack on Saudi oil installations claimed by Yemen's Iran-aligned Houthi militia.
Iran's elite Revolutionary Guards (IRGC) are "highly likely" to have facilitated attacks last Sunday on four tankers including two Saudi ships off Fujairah in the United Arab Emirates, according to a Norwegian insurers' report seen by Reuters.
A Saudi-led military coalition in Yemen carried out several air strikes on the Houthi-held capital Sanaa on Thursday.
"When tensions are this high, with the US deploying a sizeable military force, even a mistake or a tactical error by Iran could ignite the Middle East powder keg," Stephen Innes, head of trading and market strategy at SPI Asset Management, told Reuters by email.
"There are lots of supply risks with tensions this high."
Besides the drop in Iranian exports, Russian shipments have been disrupted and the North Sea - home to the crude underpinning Brent futures - is also in tighter supply owing to oilfield maintenance and outages.
The market is also awaiting a decision from the Organization of the Petroleum Exporting Countries (OPEC) and other producers over whether to continue with supply cuts that have boosted prices more than 30pc so far this year.
A meeting of an OPEC-led ministerial committee in Saudi Arabia this weekend will assess member states' commitment to their deal to reduce oil production and could make a recommendation on whether to extend or adjust the pact.
The mounting Middle East tensions overshadowed bearish developments for oil prices this week, such as an unexpected increase in US crude inventories and consistently record-high production levels.
Weekly US rig count data, an indicator of future production, will be released around 1 p.m. EDT.
Oil prices were also pressured by fears over global economic growth amid a standoff in Sino-US trade talks.
Chinese media took a hardline approach to the tariff dispute between the Washington and Beijing, saying the trade war will only make China stronger and will never bring the country to its knees.