Trump said negotiations between US and Iranian officials could resume in Pakistan in the next two days and Vice -President JD Vance, who led weekend talks that ended without a breakthrough, said he felt positive about where things stood.
"I think you're going to be watching an amazing two days ahead," Trump told ABC News reporter Jonathan Karl, adding he did not think it would be necessary to extend a two-week ceasefire that ends on April 21.
"It could end either way, but I think a deal is preferable because then they can rebuild," Trump said, according to a post by Karl on X.
"They really do have a different regime now. No matter what, we took out the radicals."
Officials from Pakistan, Iran and the Gulf also said negotiating teams from the US and Iran could return to Pakistan later this week, although one senior Iranian source said no date had been set.
Despite the optimistic note, more vessels were being turned back under the US blockade on Iranian ports, including a US-sanctioned and Chinese-owned tanker Rich Starry that was making its way back to the Strait of Hormuz on Wednesday after exiting the Persian Gulf.
Admiral Brad Cooper, the head of the US Central Command, said American forces had completely halted economic trade going in and out of Iran by sea, which he said fuelled 90 per cent of Iran's economy.
"In less than 36 hours since the blockade was implemented, US forces have completely halted economic trade going into and out of Iran by sea," Cooper said in a post on X.
Earlier, the US military said it had intercepted eight Iran-linked oil tankers since the start of the blockade on Monday, according to the Wall Street Journal.
Trump, speaking to the New York Post on Tuesday, said his negotiators were likely to be back, thanks largely to the "great job" Pakistan's army chief, Field Marshal Asim Munir, was doing to moderate the talks.
Later on Tuesday, Vance said Trump wanted to make a "grand bargain" with Iran but there was a lot of mistrust between the two countries.
"You are not going to solve that problem overnight," he said.
The signs of diplomatic engagement to end the conflict that began on February 28 helped calm oil markets, pressing benchmark prices down for a second day on Wednesday.
The war has prompted Iran to effectively shut the Strait of Hormuz, a crucial global waterway for crude and gas transport and cut shipments from the Gulf to global buyers, particularly in Asia and Europe.
About 5000 people have died in the hostilities, including about 3000 in Iran and 2000 in Lebanon.
Iran's nuclear ambitions were a key sticking point at the weekend talks.
The US had proposed a 20-year suspension of all nuclear activity by Iran, while Tehran had suggested a halt of three to five years, according to people familiar with the proposals.
The US has also pressed for any enriched nuclear material to be removed from Iran, while Tehran has demanded that international sanctions against it be removed.
One source involved in the negotiations in Pakistan said back-channel talks since the weekend had produced progress in closing that gap.
However, in a major complication for peace prospects, Israel continues to attack Lebanon as it targets Hezbollah, an Iran-backed militant group.
Israel and the US say that campaign is not covered by the ceasefire, while Iran insists it is.
On Tuesday, the UK, Canada, Japan and seven other countries condemned the killings of UN peacekeepers in Lebanon and called for "an urgent end to hostilities".
