Iran has seized two oil tankers in the Strait of Hormuz: the British-flagged Stena Impero on Friday, and the Panama-flagged MT Riah on July 14.
Iranian armed guards also reportedly boarded the Mesdar, which is Liberian-flagged but British operated, but it was eventually allowed to continue its voyage, with all crew safe and well.
Iran has claimed that it came to assistance of the MT Riah after it experienced mechanical problems.
The Guardian reported US officials saying they were unsure whether the tanker was seized by Iran or rescued.
Iran's President Hassan Rouhani suggested yesterday that his country could release the Stena Impero and its 23-strong crew if British authorities released an Iranian tanker captured off the coast of Gibraltar two weeks ago.
"If they are committed to international frameworks and abandon some actions, including what they did in Gibraltar, they will receive a proper response from Iran," Rouhani said, according to the official Islamic Republic News Agency.
Iran has claimed that the vessel had infringed maritime regulations, but the seizure was widely seen as retaliation for the July 4 capture of the Iranian tanker.
Britain has said it took control of the Iranian tanker because it was suspected of transporting oil to Syria in violation of European Union sanctions targeting Syria's government.
Tensions in the region have escalated rapidly in recent months, corresponding to Iran's increasing frustration that it is not seeing the economic benefits of a 2015 agreement to limit its nuclear programme.
US President Donald Trump pulled the US out of the deal and reimposed sanctions last year.
Iran has threatened to close the Strait if it cannot export its oil.
Early this month, Iran breached limits in the agreement on uranium enrichment, part of a process that could be used to make a nuclear weapon.
The BBC reported that the owner of the Stena Impero had made contact with the ship's master, who said that the crew were safe.