The US has launched strikes on Iran's Qeshm Island in the Strait of Hormuz, US officials have told CBS, the BBC's US partner.
Iranian state news agency IRNA reported several explosions on the island on Monday.
The US officials described the strikes as limited and said they were in response to the Iran's Islamic Revolutionary Guard Corps (IRGC) firing upon a US aircraft.
The BBC has contacted US Central Command (Centcom), the part of the US military responsible for operations in the Middle East, for comment.
It comes ahead of the US midterm elections, which will determine whether the Republicans or Democrats control Congress.
Trump has been facing falling polling numbers and pressure from within his party to end the war, which began when the US and Israel attacked Iran in February.
Earlier on Monday, he told reporters that he was in "no rush" to ramp up strikes on Iran.
"One way or the other, we will do something, but there is no rush. We crippled them financially," he told news outlet Axios. "They have no money, no gasoline and their people are getting very tired of it."
He also said the US "might need to go after Pickaxe", a site linked to Iran's nuclear programme, in an interview with Fox News on the eve of the midterm elections.
This was "not a big deal" and could be done in "one hour", Trump added.
There has been mounting speculation in the last few days that the US may resume significant strikes in Iran again after the midterms. But asked by a reporter on Monday if that was the case, Trump said "no".
Iran's foreign minister Abbas Araghchi told the IRNA earlier that "very intensive" talks to try and end the war are under way with the US via mediators.
He also said Tehran was prepared for both diplomatic and military scenarios "more than ever before" and that it was up to the US to choose between a "wise path" of negotiation or the "mistake of military aggression".
