Trump, in a post on Truth Social, said he was acting at the request of Pakistan to hold off attacks until Iranian leaders and representatives could come up with what he called a "unified proposal".
"I have therefore directed our Military to continue the Blockade and, in all other respects, remain ready and able, and will therefore extend the Ceasefire until such time as their proposal is submitted, and discussions are concluded, one way or the other," Trump said.
Iranian officials had earlier said they had yet to decide whether to attend last-ditch peace talks with the United States after US forces boarded a huge Iranian oil tanker at sea.
Trump previously said he hoped to reach a "great deal" to end the war but he did not want to extend the ceasefire, and said the US military was "raring to go" if negotiations were not successful.
Vice President JD Vance, due to lead the US delegation, had yet to board a flight for Islamabad, where the centre of the city has been locked down and a luxury hotel has been cleared out to host the talks.
A White House official said Vance would participate in additional meetings in Washington DC on Tuesday.
By the evening on Tuesday, the spokesman for Iran's foreign ministry, Esmaeil Baghaei, told state television Iran had still yet to decide whether to attend.
He described the boarding of the tanker, as well as the seizure of a separate cargo ship on Sunday, as "piracy at sea and state terrorism," which he said called into question the seriousness of the US in negotiating.
"The aggression against Iranian ships and the continued pressure indicate the continuation of the opposing side's contradictory behaviour," Baghaei said.
Pakistan's Information Minister Attaullah Tarar said in a post on X that Pakistan was still waiting for Iran's reply to its invitation: "Pakistan as the mediator is in constant touch with Iranians and pursuing the path of diplomacy and dialogue."
Earlier on Wednesday, Iranian government spokeswoman Fatemeh Mohajerani said: "We do not want to be attacked again but if such attacks occur, we will definitely respond more firmly than before," according to the state news agency IRNA.
The US military said its forces had boarded a tanker under sanctions for trading with Iran, the Tifani, in an operation that took place "without incident".
The vessel last reported its position on Tuesday morning as near Sri Lanka in the Indian Ocean, according to MarineTraffic tracking data.
It was close to fully loaded with two million barrels of crude and had signalled Singapore as its destination.
Iranian officials have publicly cited a US blockade of their ships as a reason not to negotiate.
Pakistan has been preparing to host the talks despite the uncertainty.
Nearly 20,000 security personnel have been deployed across Islamabad, officials said.
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