Crude prices on Tuesday declined for a second straight session as traders doubled down on their hopes that ongoing talks among Middle East leaders would somehow ease hostilities in that region – even though all indications were that Iran was staying true to its policies that prompted the U.S. to launch missile strikes in the first place.

Brent settled down $1.93, or 1.6 percent, at $113.88 a barrel, and West Texas Intermediate settled down $1.86, or 1.8 percent, at $99.90.

After holding talks with Saudi Arabia, Turkey, and Pakistan, the Iranian Security Council on Tuesday met its supreme leader Ayatollah Mojtaba Khamenei, with the latter reportedly emphasizing the importance of pursuing ​Iran's interests and maintaining its conditions for ending the war.

Traders apparently overlooked Tuesday’s news of the International Atomic Energy Agency warning the U.N. Security Council that it cannot verify whether Iran has diverted nuclear material, and that Tehran has repeatedly refused to grant inspection access.

Also, the British Home Office on Tuesday in updating its travel advisory for Iran warned of a high risk of sudden escalation of hostilities and described the situation as “deeply unpredictable.”

However, transit through the Strait of Hormuz having been restored to near pre-war levels may explain why continued violence in the Middle East – chiefly, Iran-backed Houthis claiming  they had struck Saudi Arabia’s Ras Tanura oil refinery with a ballistic missile - also didn’t dent investor optimism.

Gelber & Associates analysts wrote in a note, "Continued Houthi attacks on Saudi Arabia and the expanding military presence in the Gulf are keeping supply ​risks in place, even as diplomatic headlines encourage some of the recent premium to unwind."

Israeli prime minister ​Benjamin Netanyahu’s re-election on Tuesday caused analysts such as those at Commerzbank to ponder if this means he “might attempt to achieve regime change in Iran”; indeed, Bjarne Schieldrop, analyst at SEB, remarked, "The impression now is that there is a significant risk premium in crude oil prices for the risk that the US/Israel will attack Iran in the coming weeks."

Taking a bird’s eye view of the U.S./Iran war and its effects on Tuesday was Giovanni Staunovo, analyst at UBS, who said global oil inventories have fallen by around 500 million barrels since February; Brent is expected to remain near $110 per barrel for the rest of the year; and “increased ship-to-ship transfers required to cross the Strait of Hormuz are absorbing tanker capacity.”

Staunovo concluded, “With global visible oil inventories at multi-year lows and likely to take time to rebuild once the conflict is resolved, oil prices may also remain higher for longer as inventories first need to be replenished.”