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NEW YORK, July 6 (Reuters) - Oil prices were little changed on Monday, with crude trading at levels last seen before the outbreak of the Iran war, as Saudi Arabia cut its official selling prices, the OPEC+ alliance agreed to a new increase in production targets from August, and exports through the Strait of Hormuz rose.

Brent crude futures rose seven cents , or 0.1 percent, to $ 72.19 a barrel by 1626 GMT. The benchmark hit a four-year high above $126 in late April . U.S. West Texas Intermediate crude futures climbed 12 cents , or 0.2 percent, to $ 68.81 a barrel.

There was no settlement for U.S. crude contracts on Friday, when U.S. markets were closed a day before the Independence Day holiday.

The two crude oils saw little change last week, after mostly falling in the past few weeks to levels not seen since late February, before the outbreak of the war that caused major disruption to global energy flows.

"This downward trend is still being influenced by the departure of oil tankers from the Gulf where they were stuck, which has increased the amount of oil in the water," said Giovanni Staunovo, an analyst at UBS.

Investors are closely watching talks between the United States and Iran regarding the fate of navigation through the Strait of Hormuz, as they anticipate a recovery in oil exports from the Gulf.

Two sources familiar with the matter said on Monday that the United Arab Emirates has increased its crude oil production to near record highs, exceeding 3.8 million barrels per day in June, after withdrawing from the Organization of the Petroleum Exporting Countries (OPEC) to eliminate production restrictions.

Saudi Arabia set the official selling price for its flagship crude, Arab Light, to Asia for August at $1.50 a barrel below the Oman/Dubai average, marking the largest monthly price cut since Reuters began tracking the price in 2003.

Traders told Reuters that Abu Dhabi National Oil Company (ADNOC) is selling crude oil at discounts during tenders.

The OPEC+ alliance, which includes OPEC and allies including Russia, agreed on Sunday to increase production targets by 188,000 barrels per day starting in August, on top of similar increases in June and July.

However, this increase remained largely on paper only because of the US-Israeli war on Iran, which closed the Strait of Hormuz to oil tanker traffic from major OPEC producers, such as Saudi Arabia, Kuwait and Iraq, thus limiting their production.