Iran's semi-official Tasnim news agency said the Revolutionary Guards had seized two vessels for maritime violations and escorted them to Iranian shores.
It was the first time Iran has seized ships since the beginning of the war on February 28.
Earlier, a British maritime security agency reported three ships had come under fire.
Trump said on social media late on Tuesday that the US had agreed to a request by Pakistani mediators "to hold our Attack on the Country of Iran until such time as their leaders and representatives can come up with a unified proposal ... and discussions are concluded, one way or the other".
But even as he announced what appeared to be a unilateral ceasefire extension, Trump also said he would continue the US Navy's blockade of Iran's trade by sea.
The United States fired on and seized an Iranian cargo vessel on Saturday and boarded a huge Iranian oil tanker on Tuesday in the Indian Ocean.
Iran considers the US blockade an act of war and has said it will not lift its closure of the strait, which has caused a global energy crisis, as long as the US blockade continues.
Pakistan, acting as mediator, had cleared out a luxury hotel in the capital Islamabad for last-ditch peace talks on Tuesday, in the hopes of reaching a deal in the final hours before a two-week-old ceasefire expired.
But Iran never confirmed it would attend and a US delegation led by Vice-President JD Vance never departed Washington, leaving an apparent stalemate in the nearly two-month war with no clear solution to reopen the Strait of Hormuz.
There was no response early on Wednesday to Trump's ceasefire announcement from senior Iranian officials, although some initial reactions from Tehran suggested Trump's comments were being treated sceptically.
Tasnim said Iran had not asked for a ceasefire extension and repeated threats to break the US blockade by force.
Throughout the war, Iran has effectively shut the strait to ships other than its own by attacking vessels that attempt to transit without its permission.
About a fifth of global oil and liquefied natural gas usually passes through the waterway.
On Wednesday, British maritime security agency UKMTO said at least three container ships had reported being hit by gunfire in the strait.
The master of one ship reported being approached by an Iranian gunboat northeast of Oman on Wednesday, the agency said.
Two other ships had said they came under fire west of Iran with no reported injuries.
Iran has condemned the US Navy intercepting Iranian ships at sea as part of its blockade, including a huge tanker bound for Singapore that was boarded in the Indian Ocean on Tuesday hours before peace talks had been due to resume.
With his announcement on Tuesday, Trump again pulled back at the last moment from warnings to bomb Iran's power plants and bridges, a threat condemned by the United Nations and others as potentially constituting war crimes.
Oil prices fell below $US100 on Wednesday following the ceasefire announcement, even as the tentatively scheduled peace talks in Islamabad seemed on the verge of falling apart.
Before Trump's latest announcement, a senior Iranian official had told Reuters that Iran's negotiators had been willing to attend another round of talks, but only if the US abandoned a policy of pressure and threats.
A first session of talks 11 days ago produced no agreement, with the United States focusing on a longstanding dispute over Iran's stockpiles of highly enriched uranium.
Trump wants to take it out of Iran to prevent Tehran enriching it further to the point where it could be used to make a nuclear weapon.
Iran says it has only a peaceful civilian nuclear program.
