Trump maintained the US Navy blockade of Iran's trade by sea on Wednesday, and Iran's parliament speaker and top negotiator Mohammad Baqer Qalibaf said a full ceasefire only made sense if it was lifted.
Reopening the strait was impossible with such a "flagrant breach of the ceasefire," Qalibaf said in his first response to Trump's ceasefire extension on X.
"You did not achieve your goals through military aggression and you will not achieve them by bullying either. The only way is recognising the Iranian people's rights," he said in his first response to Trump's ceasefire extension.
Iran's semi-official Tasnim news agency earlier 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 war began at the end of February.
The Revolutionary Guards also warned that any disruption to order and safety in the strait would be considered a "red line", Tasnim said.
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."
A source briefed on the matter confirmed on Wednesday that Trump had not set a timeline for the extension of the ceasefire.
In a show of defiance, Iran showcased some of its ballistic weapons at a parade in Tehran on Tuesday evening, with images on state TV showing large crowds waving Iranian flags and a banner in the background with a fist choking off the strait.
Captions read: "Indefinitely under Iran's Control" and "Trump could not do a damn thing", referring to the waterway, the closure of which has caused a global energy crisis.
Pakistan, which has acted as a mediator, was still trying to bring the sides together for negotiations after both failed to show up for talks on Tuesday before the two-week-old ceasefire had been due to expire.
"We were all prepared for the talks, the stage was set," a Pakistani official briefed on the preparations told Reuters.
"If you ask me honestly, it was a setback we were not expecting, because the Iranians never refused, they were up to come and join, and they still are."
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. Around a fifth of global oil and liquefied natural gas normally passes through the waterway.
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. Iran had said it would strike its Arab neighbours if its civilian infrastructure was hit.
Oil prices reversed course to head higher after the shipping incidents on Wednesday, with Brent crude futures up almost four per cent at $US102.2 ($A142.8) a barrel.
A first session of peace talks 11 days ago produced no agreement.
Washington wants Iran to give up highly enriched uranium and forgo further enrichment to prevent it getting a weapon.
Iran, which says its nuclear program is peaceful, wants an end to the war, the lifting of sanctions, reparations for damage and recognition of its control over the strait.
