NEW YORK, June 25 (Reuters) - Oil prices edged up about 2% on Thursday after a cargo vessel was hit by an unknown projectile near Oman, sparking worries about how long it could take for oil flows in the Middle East to return to levels seen before the U.S.-Israeli war on Iran.

Earlier in the session, crude futures fell to their lowest levels since February 27, the day before the war began, as crude shipments through the strait rose to their highest since the start of the war. Before the war, about 20% of world oil supplies passed through the Strait of Hormuz between Iran and Oman.

Brent futures rose $1.12, or 1.5%, to $74.86 a barrel at 1:40 p.m. EDT (1740 GMT), while U.S. West Texas Intermediate crude rose $1.22, or 1.7%, to $71.56.

On Wednesday, U.S. Energy Secretary Chris Wright said flows through the Strait of Hormuz were close to pre-war levels. But he said normalisation would take a few weeks because mines must be removed from the strait.

But on Thursday, a cargo ship reported a suspected attack as it attempted to pass through the Strait of Hormuz close to the coast of Oman, according to the UK Maritime Trade Operations.

"Storage tanks across the Gulf are around 50% to 60% full, so if tanker traffic through the strait does not pick up in the near term, producers will need to throttle back output, and the full recovery moves into next year," analysts at consultancy Rystad Energy said in a report.

The agreement between the U.S. and Iran to end the war has allowed the resumption of traffic through the strait, which Iran had effectively blockaded. 

It set up a 60-day period of negotiations to tackle tougher issues, such as Iran's nuclear programme. U.S. Secretary of State Marco Rubio told Gulf allies on Thursday that any deal with Iran would take their interests into account, as he wrapped up a Middle East trip aimed at winning over regional partners with deep reservations about the preliminary accord.

Goldman Sachs said it does not expect a large pick-up in Iranian production, even if sanctions relief extends beyond the August 21 expiry.

On the demand side, China is likely to remain the main buyer of Iranian crude, as European Union and British sanctions on Iranian oil and vessels remain in place, the bank added.

UBS lowered its Brent price forecasts to $85 per barrel for end-September and end-December, and $80 per barrel for end-March and end-June 2027.

TECHNICAL BUYING

In addition to worries about ship traffic through the Strait of Hormuz, analysts noted crude prices also rose with some technical buying.

"Today's strength appears tied to short covering and bargain buying after the market became increasingly oversold following the rapid collapse from recent highs," energy consulting firm Gelber & Associates said in a note.

Despite small price increases on Thursday, both markets have remained deep in technically oversold territory for more than a week.

AROUND THE WORLD

In Venezuela, thousands were feared dead on Thursday after two powerful earthquakes wreaked havoc in and around the capital Caracas, trapping people beneath the rubble of collapsed buildings and setting off powerful aftershocks.

Those earthquakes could slow the increase in Venezuelan oil exports expected by U.S. President Donald Trump's administration after the U.S. captured Venezuela's President Nicolas Maduro in January.

Iraq, meanwhile, has considered leaving the Organization of the Petroleum Exporting Countries (OPEC) if the group does not allow Baghdad to significantly increase oil production, sources with knowledge of the matter told Reuters.

The prospect of Iraq leaving would be a serious blow to OPEC, which saw the United Arab Emirates walk away less than two months ago.