Neither side offered any specifics about the state of negotiations on Saturday, days before a fragile ceasefire in the US-Israeli war against Iran is set to expire.
The war, now in its eighth week, has killed thousands of people, spread to Israeli attacks in Lebanon and sent oil prices surging because of the de facto closure of the strait, which before the war carried one-fifth of the world's oil shipments.
"We have had progress but there is still a big distance between us," Iran's chief negotiator, Mohammad Baqer Qalibaf, told state media, referring to talks last weekend.
"There are some issues on which we insist ... They also have red lines. But these issues could be just one or two."
Trump said the US was having "very good conversations" but gave no other details.
Tehran reversed course on Saturday to reassert control over the strait, again closing the energy choke point and adding fresh uncertainty to the war, which the US and Israel launched on February 28.
Iran said it was responding to a continued US blockade of Iranian ports, calling it a violation of the ceasefire, while Supreme Leader Ayatollah Mojtaba Khamenei said Iran's navy was ready to inflict "new bitter defeats" on its enemies. Trump called the move "blackmail" even as he praised the talks.
On Friday, Iran had announced the temporary reopening of the Strait of Hormuz following a separate US-brokered 10-day ceasefire agreement on Thursday between Israel and Lebanon.
Trump defended the US blockade and threatened "to start dropping bombs again" unless the countries reached a long-term deal before the ceasefire expires on Wednesday.
Concern remained after at least two vessels reported being attacked on Saturday while trying to transit the waterway. India summoned the Iranian ambassador in New Delhi and expressed deep concern that two Indian-flagged ships had come under fire in the strait, the government said.
US Central Command said American forces were enforcing a maritime blockade of Iran but did not comment on the latest Iranian actions.
Tehran's reversal raised the risk that oil and gas shipments through the strait could remain disrupted just as Trump weighs whether to extend the ceasefire.
When American and Iranian negotiators met last weekend in Islamabad, the US proposed a 20-year suspension of all Iranian nuclear activity, while Iran suggested a halt of three to five years, according to people familiar with the proposals.
Iran's deputy foreign minister, Saeed Khatibzadeh, said no date had been set for the next round of negotiations, adding that a framework of understanding must be agreed first.
Trump on Friday said there could be talks this weekend and that the two sides were "very close to making a deal."
There were no signs on Saturday of preparations for new talks in the Pakistani capital, where the highest-level US-Iran negotiations since the 1979 Islamic Revolution ended without agreement last weekend.
Senior national security aides gathered at the White House on Saturday morning. Trump later went to the Trump National Golf Club with top envoy Steve Witkoff, one of his Iran negotiators.
Pressure for a way out of the war has mounted as Trump's fellow Republicans defend narrow majorities in Congress in the November midterm elections with US gasoline prices high, inflation rising and his own approval ratings down.
