A US official on Monday said there was continued engagement with Iran, and forward motion on trying to get to an agreement. Pakistan Prime Minister Shehbaz Sharif also said efforts were still under way to resolve the conflict.
But oil prices climbed back to $US100 ($A141) per barrel, with no sign of a swift reopening of the Strait of Hormuz to ease the biggest-ever disruption in supplies and broader concerns over the durability of a two-week ceasefire agreement reached last week.
US President Donald Trump said Iran had been in touch on Monday and wanted to make a deal but that he would not sanction any agreement allowing Tehran to have a nuclear weapon.
"Iran will not have a nuclear weapon," Trump told reporters at the White House.
"We can't let a country blackmail or extort the world."
Since the US and Israel began the war on February 28, Iran effectively shut the Strait of Hormuz to all vessels except its own, saying passage would be permitted only under Iranian control and subject to a fee.
Trump has said Washington would block Iranian vessels and any ships that paid such tolls and that any Iranian "fast-attack" ships that went near the blockade would be eliminated.
Brigadier General Reza Talaei-Nik, a spokesperson for Iran's Ministry of Defence, warned that foreign military efforts to police the strait would escalate the crisis and instability in global energy security.
NATO allies including Britain and France said they would not be drawn into the conflict by taking part in the blockade, stressing instead the need to reopen the waterway, through which about one-fifth of the world's oil normally passes.
The talks between the US and Iran in Pakistan, the first direct meeting in more than a decade and the highest-level discussions since the 1979 Islamic Revolution, ended on Sunday without an agreement.
Despite that, Vice President JD Vance, who led the US delegation, told Fox News on Monday the US "made a lot of progress" by communicating to Tehran where the US "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.
The ceasefire that halted six weeks of US and Israeli airstrikes looked in jeopardy, with only a week left to run.
The US military's Central Command said the blockade would be "enforced impartially against vessels of all nations" entering or leaving Iranian ports in the Gulf and Gulf of Oman.
"The blockade will not impede neutral transit passage through the Strait of Hormuz to or from non-Iranian destinations," Central Command said in a note to seafarers seen by Reuters on Monday.
An Iranian military spokesperson 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 said Iran's navy had been "completely obliterated" during the war, adding that only a small number of "fast-attack ships" remained.
"Warning: If any of these ships come anywhere close to our BLOCKADE, they will be immediately ELIMINATED, using the same system of kill that we use against the drug dealers on boats at Sea. It is quick and brutal," Trump said on social media.
He was apparently referring to the US strikes carried out against suspected drug boats in the Caribbean and Pacific. The strikes, which began in September, killed more than 160 people. The US military has not provided evidence that the vessels were ferrying drugs.
