By Colleen Howe and Sam Li

(Reuters) -Oil prices surged on Thursday after Israel said it attacked Iranian nuclear sites in Natanz and Arak overnight and as investors grappled with fears of a broader conflict in the Middle East that could disrupt crude supplies.

Brent crude futures rose 88 cents, or 1.15%, to $77.58 a barrel by 0708 GMT, after gaining 0.3% in the previous session when high volatility saw prices fall as much as 2.7%.

U.S. West Texas Intermediate crude for July rose $1.11, or 1.48% to $76.25 a barrel, after settling up 0.4% in the previous when it dropped as much as 2.4%.

The July contract expires on Friday and the more active August contract rose 92 cents, or 1.25%, to $74.42 a barrel.

There is still a "healthy risk premium baked into the price as traders await to see whether the next stage of the Israel-Iran conflict is a U.S. strike or peace talks", Tony Sycamore, market analyst at IG, said in a client note.

Goldman Sachs on Wednesday said a geopolitical risk premium of about $10 a barrel is justified given lower Iranian supply and risk of wider disruption that could push Brent crude above $90.

Trump on Wednesday told reporters that he may or may not decide whether the U.S. will join Israel in its attacks on Iran. The conflict stretched into its seventh day on Thursday.

As a result of the unpredictability that has long characterised Trump's foreign policy, "markets remain jittery, awaiting firmer signals that could influence global oil supply and regional stability," said Priyanka Sachdeva, senior market analyst at Phillip Nova.

The risk of major energy disruptions will rise if Iran feels existentially threatened, and the U.S. entry into the conflict could trigger direct attacks on tankers and energy infrastructure, said RBC Capital’s analyst Helima Croft.

Iran is the third-largest producer among members of the Organization of the Petroleum Exporting Countries, extracting about 3.3 million barrels per day (bpd) of crude oil.

About 19 million bpd of oil and oil products move through the Strait of Hormuz along Iran's southern coast and there is widespread concern the fighting could disrupt trade flows.

Separately, the U.S. Federal Reserve kept its interest rates steady on Wednesday but pencilled in two cuts by the end of the year. Chair Jerome Powell said cuts would be "data-dependent" and that it expects accelerated consumer inflation from Trump's planned import tariffs.

Lower interest rates would stimulate the economy, and as a result demand for oil, but that could exacerbate inflation.

(Reporting by Colleen Howe and Sam Li; Editing by Christian Schmollinger, Christopher Cushing and Shri Navaratnam)

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