Oil prices edged higher on Tuesday, but gains were limited as traders looked beyond easing geopolitical tensions in the Middle East and turned their attention to ​supply increases and demand prospects.

Brent crude futures gained 28 cents, or 0.39%, ‌to $72.29, and U.S. West Texas Intermediate crude rose to $68.84 a barrel, up 29 cents, or 0.26%, as of 0046 GMT, after settling down to around pre-Iran war levels on Monday.

"The steps towards recovery ​in supply have eased the immediate risk premium, but the market remains ​wary of putting too much faith in the stability of the current ⁠truce given the on-again-off-again nature of U.S.-Iran relations," said Tim Waterer, ​chief market analyst at KCM Trade.

President Donald Trump said on Monday the United States would ​either reach a deal with Iran or "finish the job," renewing his threat of military action as Tehran projects defiance following the funeral of former Supreme Leader Ayatollah Ali Khamenei.

Investors have been keeping a close eye ​on talks between the U.S. and Iran over the fate of shipping through ​the Strait of Hormuz while tracking the recovery in Gulf oil exports.

The United Arab Emirates raised crude output ‌above ⁠3.8 million bpd in June, its highest since April 2020 and above pre-Iran war levels, after leaving OPEC+ production quotas in May, according to Reuters estimates.

"We will be watching for early signs of demand response, particularly from China. The market has priced in ​a lot of ​the positive supply news, ⁠so the next leg in oil prices will depend on whether physical reality matches the optimistic headlines," Waterer added.

The Organisation of ​the Petroleum Exporting Countries and its allies including Russia agreed on Sunday ​to further ⁠increase output targets by 188,000 bpd from August, on top of similar increases for June and July.

Saudi Arabia cut the August official selling price (OSP) for its flagship Arab Light crude ⁠to Asia ​to $1.50 a barrel below the Oman/Dubai average, an $11 ​cut from the previous month and the biggest drop in more than two decades, according to a Saudi ​Aramco pricing statement released on Monday.