US President Donald Trump says he has instructed negotiators "not to rush into a deal" with Iran, after reports suggested an agreement was close.

According to US media, the deal under discussion involves a 60-day ceasefire extension, reopening the Strait of Hormuz and further negotiations over Iran's nuclear programme.

In a social media post, Trump said "constructive" talks were proceeding, but "both sides must take their time and get it right".

Trump said on Saturday an agreement had been "largely negotiated", prompting speculation an announcement could be imminent.

Reports in Iranian media say there are still "one or two" points of disagreement in the potential deal.

Iranian officials had similarly signalled progress in talks over the weekend, but foreign ministry spokesperson Esmail Baghaei said that did not mean agreements would be reached on key issues.

The mooted deal has split Republicans, with some publicly arguing it is too lenient on Iran.

Senator Ted Cruz said it would be "a disastrous mistake", while Roger Wicker, who chairs the Senate Armed Services Committee, said a 60-day ceasefire would mean "everything accomplished by Operation Epic Fury would be for nought!"

But Representative Mike Lawler, who sits on the House Foreign Affairs Committee, said the administration has managed to "force the remnants of this regime into a negotiation, a real negotiation".

The US and Israel launched wide-ranging strikes on Iran on 28 February, sparking conflict across the Middle East. Iran responded by launching attacks on Israel and US-allied states in the Gulf.

A ceasefire agreed in April meant to facilitate talks has largely been observed, despite occasional exchanges of fire.

In Sunday's post on Truth Social, Trump said negotiations "are proceeding in an orderly and constructive manner, and I have informed my representatives not to rush into a deal, as time is on our side".

"Both sides must take their time and get it right. There can be no mistakes!"

Trump also said Iran "must understand" it cannot develop a nuclear weapon, a stance he has frequently reiterated and that is shared by Israel and other Western allies.

The US and its allies suspect that Iran is seeking to develop a nuclear weapon - but Tehran has said its nuclear programme is solely for peaceful purposes.

Some reports in US media suggest the deal under discussion would also see Iran hand over its highly-enriched uranium.

It is thought to have about 440kg (970 lbs) of highly-enriched uranium, which is a metal that can be used to create nuclear energy and - when enriched sufficiently - weapons.

In his social media post, the US president also said Washington's blockade of Iranian ports- which has been in place since early April - will remain "in full force and effect until an agreement is reached, certified, and signed".

The US has been enforcing its blockade to pressure Tehran into agreeing to its terms.

For its part, Iran has continued to control the Strait of Hormuz, effectively closing the vital waterway through which around 20% of the world's oil and liquefied natural gas travels. The move has sent oil prices soaring globally.

US Secretary of State Marco Rubio earlier said that "significant" but "not final" progress had been made in the negotiations.

He hinted at good news on Hormuz, saying that progress over the past 48 hours could result in a "completely open strait... without tolls".

On Saturday, Baghaei told state television that Iran was in the process of finalising a "memorandum of understanding" which would allow additional talks so that "ultimately a final agreement can be reached".

Trump also mentioned a "memorandum of understanding" in a Truth Social post on Saturday.

Pakistan's Deputy Prime Minister Ishaq Dar, who has been mediating talks, has said that recent negotiations are "grounds for optimism" that a positive outcome is "within reach".

Some US media outlets reported that no agreement between the two countries was expected to be signed on Sunday, citing officials.