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.
"You should stay there, really, because something could be happening over the next two days, and we're more inclined to go there," Trump was quoted by the New York Post as saying.
Later at an event in Georgia on Tuesday, US time, Vice President JD 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," Vance said.
While the US blockade drew angry rhetoric from Iran, signs that diplomatic engagement might continue helped to calm oil markets, pushing benchmark prices below $US100 per barrel.
Iran has effectively shut the Strait of Hormuz, a crucial global waterway for oil and gas transport, since the war began on February 28. Roughly 5000 people have died in the hostilities.
Talks in Islamabad last weekend did not yield an agreement, raising doubts over the survival of a two-week ceasefire that still has a week to run.
Iran's nuclear ambitions were a key sticking point. 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.
One source involved in the negotiations in Pakistan said backchannel talks since the weekend had produced progress in closing that gap, bringing the two sides closer to a deal that could be put forward at a new round of talks.
US Central Command said no ships made it past its blockade of Iranian ports in the first 24 hours it was in place, while six merchant vessels turned back.
However, shipping data showed the blockade had made little difference to Strait of Hormuz traffic on Tuesday, with at least eight ships crossing the waterway.
The International Monetary Fund cut its growth outlook and said the global economy would teeter on the brink of recession if the conflict worsens and oil stays above $US100 into 2027.
The International Energy Agency lowered its forecasts for global oil supply and demand growth.
The United States' NATO allies including Britain and France said they would not be drawn into the conflict by taking part in the blockade, although they have offered to help safeguard the strait when an agreement is in place.
Analysts say oil prices are likely to remain elevated for weeks after the strait is fully reopened, due to backlogs, damaged infrastructure and elevated uncertainty.
Further complicating prospects for peace, Israel has continued to attack Lebanon as it targets Hezbollah, an Iran-backed militant group.
In Washington, US Secretary of State Marco Rubio hosted a meeting between envoys for Israel and Lebanon, which the State Department described as the first major high-level engagement between the two countries since 1993.
The US State Department said afterwards the two sides agreed to continue their talks.
Israel's ambassador to the US said he was hopeful the Lebanese government wanted to reduce Hezbollah's influence, while Lebanon's ambassador to the US said in a statement the meeting was "constructive," and the date and location of the next meeting would be announced in due course.
