While the US blockade drew angry rhetoric from Tehran, signs that diplomatic engagement might continue helped calm oil markets, pushing benchmark prices below $US100 on Tuesday.
The highest-level talks between the two adversaries since the 1979 Islamic Revolution ended in the Pakistani capital without a breakthrough at the weekend, raising doubts over the survival of a two-week ceasefire that still has a week to run.
But a source involved in the talks said on Tuesday both countries could return as early as the end of the week, and that a proposal had been shared with Washington and Tehran to resend their delegations.
"No firm date has been set, with the delegations keeping Friday through Sunday open," a senior Iranian source said.
US President Donald Trump said Iran had been in touch on Monday and wanted to make a deal, adding that he would not sanction any agreement that allowed Tehran to possess a nuclear weapon.
Since the United States and Israel began the war on February 28, Iran effectively shut the Strait of Hormuz to nearly all vessels except its own, saying passage would be permitted only under Iranian control and subject to a fee.
The fallout has been widespread, as nearly a fifth of the world's oil and gas previously flowed through the narrow waterway.
In a countermeasure, the US military said it began blocking shipping traffic in and out of Iran's ports on Monday.
Tehran has threatened to hit naval ships going through the strait and to retaliate against its Gulf neighbours' ports.
The US blockade has further clouded the outlook for global energy security and the supply of a vast array of goods that rely on petroleum.
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.
French President Emmanuel Macron and British Prime Minister Keir Starmer will chair a video conference on Friday for countries willing to contribute to a defensive mission to restore freedom of navigation in the strait when security conditions permit.
China, the main buyer of Iranian oil, said the US blockade was "dangerous and irresponsible" and would only aggravate tensions.
US Vice-President JD Vance, who led Washington's delegation opposite Iran's speaker of parliament, Mohammad Baqer Qalibaf, told Fox News on Monday the US had "made a lot of progress" by communicating to Tehran where Washington "could make some accommodation" and where it would remain inflexible.
He said Trump was adamant that any enriched nuclear material must be removed from Iran and a mechanism must be established to verify that Iran is not developing nuclear weapons.
Tehran "moved in our direction, which is why I think we would say that we had some good signs, but they didn't move far enough", Vance said.
With the war unpopular at home and rising energy prices causing political blowback, Trump paused the US-Israeli bombing campaign last week after threatening to destroy Iran's "whole civilisation" unless it reopened the strait.
The ceasefire, which halted US-Israeli strikes and fire from Iran across the Gulf in response, has largely held in its first week despite sharp rhetoric from both sides.
Iran's military called any US restrictions on international shipping "piracy", warning that if Iranian ports were threatened, no port in the Gulf or Gulf of Oman would be secure.
Any military vessels approaching the strait would violate the ceasefire, Iran's Revolutionary Guards said.
Trump warned on social media that if any of Iran's remaining naval ships approached the US blockade, they would be eliminated.
