They built a small anti-aircraft system and we destroyed it in about 15 minutes, maybe five minutes," Trump told reporters as he left Florida in response to a question about the Keshm explosion.
According to the "Tasnim" news agency, two rockets hit Keshem Island on Saturday morning.
Referring to the negotiations with the Islamic Republic, Trump said: "We are interacting with the Iranians." We'll see what the result of all this will be."
He said: "We have made great progress in relation to Iran. Now we produce more oil than before the war. This is not a war. "When no one is injured or killed or anything like that for five months, you can't call it a war."
Earlier, an official at the US military's Central Command (CENTCOM) told the Al Jazeera news channel that the situation around the island was "relatively calm" in response to reports of the explosion on Kesham Island.
Confirming Centcom's knowledge of the reports, he declined to elaborate. Iran's official media reported earlier that two missiles hit Kashem.