Oil remains on track for a second straight weekly decline, but signs of cracks in the agreement to end the war have given traders pause.
Jet fuel may stay expensive for months, and airlines know travelers are willing to pay more for tickets.
Drivers are enjoying some relief at the pump after the United States and Iran signed an agreement to reopen the Strait of Hormuz.
Traders are waiting for U.S. and Iranian officials to meet in Switzerland on Friday, when they are expected to sign an initial agreement and begin a 60-day cease-fire.
Stocks were mixed after strong rallies the day before.
The preliminary agreement may not have an immediate effect on prices at the pump. Damaged infrastructure and risky transport could keep costs up.
The pace of the recovery will depend on how confident companies are that the deal between the United States and Iran will hold and be extended.
The amount of oil and fuel stored by businesses and governments has fallen sharply since the start of the U.S.-Israeli war against Iran.
The attacks, which strained a two-month cease-fire between Iran and the United States, were the latest jolt to energy markets.
Oil prices fell after Israel and Iran agreed to halt strikes against each other, easing fears of a broader regional conflict that had briefly driven crude higher.