July 7 (Reuters) - Oil prices rose on Tuesday, but gains were limited as traders shifted their focus to supply growth and demand prospects, ignoring easing geopolitical tensions in the Middle East.

Brent crude futures rose 28 cents, or 0.39 percent, to $72.29 a barrel by 00:46 GMT, while U.S. West Texas Intermediate crude futures climbed 29 cents, or 0.26 percent, to $68.84 a barrel, after settling on Monday at levels close to those seen before the Iran war.

Tim Waterer, senior market analyst at KCM Trade, said, "The steps taken to recover supplies have helped to ease the immediate risk premium, but the market remains wary of betting too much on the stability of the current truce, given the volatile nature of US-Iranian relations."

US President Donald Trump said on Monday that the United States would either reach an agreement with Iran or "finish the job," repeating his threat of military action at a time when Tehran is defiant following the funeral of the late Supreme Leader Ayatollah Ali Khamenei.

Investors are closely monitoring talks between the United States and Iran to determine the fate of shipping traffic through the Strait of Hormuz, as well as the recovery of Gulf oil exports.

Reuters estimates showed that the UAE raised its crude production to more than 3.8 million barrels per day in June, the highest level since April 2020 and exceeding pre-Iran war levels, after leaving the OPEC+ alliance in May.

The Organization of the Petroleum Exporting Countries (OPEC) and its allies, including Russia, agreed on Sunday to increase production targets by 188,000 barrels per day starting in August, along with similar increases approved for June and July.