The escalation came as Washington awaited Tehran's response to a US proposal to end the war, which began on February 28 when the US and Israel launched air strikes on Iran.
Trump said on Thursday that three US Navy destroyers were attacked as they moved through the Strait of Hormuz, a conduit for about a fifth of the world's oil and liquefied natural gas flows that Iran has all but closed since the conflict began.
"Three World Class American Destroyers just transited, very successfully, out of the Strait of Hormuz, under fire. There was no damage done to the three Destroyers, but great damage done to the Iranian attackers," Trump wrote on Truth Social.
He later told reporters the ceasefire remained in effect and played down the exchange.
"They trifled with us today. We blew them away," Trump said in Washington.
Iran, however, accused the United States of breaching the ceasefire, an agreement that has been punctuated by intermittent clashes since it was announced on April 7.
Iran's top joint military command said US forces had targeted an Iranian oil tanker and another ship, and carried out air attacks on civilian areas on Qeshm Island in the Strait of Hormuz and nearby coastal areas.
It said Iranian forces responded by attacking US military vessels east of the strait and south of the port of Chabahar.
A spokesperson for Iran's Khatam al-Anbiya Central Headquarters said the Iranian strikes inflicted "significant damage", but US Central Command said none of its assets were hit.
Iranian state media later signalled a de-escalation, with Press TV reporting that, after several hours of exchanges, "the situation on Iranian islands and coastal cities by the Strait of Hormuz is back to normal now."
The confrontation was not confined to the waterway.
The United Arab Emirates said its air defences were engaging missile and drone threats from Iran early on Friday, although details were scarce.
Since the war began, Iran has repeatedly targeted the UAE and other Gulf states that host US military bases.
Oil prices rose in early trade in Asia on Friday, with Brent crude futures rising above $US100 a barrel after the latest clashes.
China, which has remained a major buyer of Iranian oil since the outbreak of the war, on Friday confirmed that an oil products tanker carrying Chinese crew was attacked near the strait on Monday.
Trump said diplomacy was still on track despite Thursday's hostilities, telling reporters, "We're negotiating with the Iranians."
Before the latest clashes, the US had floated a proposal that would formally end the conflict, but did not address two of its core demands - that Iran suspend its nuclear program and reopen the strait.
Tehran said it had not yet reached a decision on the plan.
Even so, Trump said Tehran had acknowledged his demand that Iran could never get a nuclear weapon, a prohibition he said was implicit in the US proposal.
Asked when any deal might be reached, Trump said, "It might not happen, but it could happen any day. I believe they want to deal more than I do."
The war has tested Trump's relationship with his US base of supporters, after he had campaigned against involving the United States in foreign wars and promised to bring down fuel prices.
