US President Donald Trump has said the month-long ceasefire between the US and Iran is on "massive life support".

He told reporters in the Oval Office on Monday that while the ceasefire remained in place, it was "unbelievably weak".

Iran laid out its demands to end the war and reopen the Strait of Hormuz in a counter-offer sent to the US on Sunday. Trump rejected the proposal, calling it "totally unacceptable" and a "piece of garbage".

Esmail Baghaei, a foreign ministry spokesperson for Iran, responded by saying Tehran's proposals were "responsible" and "generous".

Tehran's offer includes an immediate end to the war on all fronts - a reference to the continued Israeli attacks against Iran-supported Hezbollah in Lebanon - a halt to the US naval blockade of Iranian ports and guarantees of no further attacks on Iran, according to Iran's semi-official Tasnim news agency.

It also reportedly includes a demand for compensation for war damage and an emphasis on Iranian sovereignty over the Strait of Hormuz.

Trump criticised the proposal, writing on Truth Social on Sunday: "I have just read the response from Iran's so-called 'Representatives.' I don't like it - TOTALLY UNACCEPTABLE."

In response to Trump's comments, Baghaei said Iran would act "in any way necessary to secure our interests".

Speaking in the Oval Office later on Monday, Trump addressed the ceasefire between the two countries which has largely been observed since April despite occasional exchanges of fire.

He told reporters: "I would say the ceasefire is on massive life support... when the doctor walks in and says, 'Sir, your loved one has approximately a 1 percent chance of living'."

The US president said Iran's leaders were "very dishonourable people", adding: "Look, I've had to deal with them four or five times - they change their mind."

"That piece of garbage they sent us - I didn't even finish reading it," he said.

Trump also accused Iran of going back on an agreement to allow the US to remove its supply of enriched uranium. He insisted that Iran would "never have a nuclear weapon".

Iran's Tasnim news agency quoted a source close to the negotiating team as saying: "There is no such thing in Iran's proposal as accepting taking out enriched nuclear material."

Earlier this week, Trump repeated that the war in Iran will be "over quickly".

But Israeli Prime Minister Benjamin Netanyahu said that Iran's stockpile of enriched uranium must be "taken out" before the war can be considered over.

"There's still enrichment sites that have to be dismantled," Netanyahu said in an interview on CBS's 60 Minutes show.

US news outlet Axios reported that the initial one-page, 14-point US memorandum includes provisions such as a suspension on Iranian nuclear enrichment, the lifting of sanctions, and restoring free transit through the Strait of Hormuz.

It cited two US officials and two other sources - all unnamed - who it described as briefed on the issues. These sources were reported as saying that many of the terms laid out in the memo would be contingent on a final agreement being reached.

Iran has continued to block the Strait of Hormuz, prompting a rise in world oil prices. Normally about 20% of the world's oil and liquefied natural gas passes through the strait.

The US, for its part, has been enforcing a blockade of Iranian ports to exert pressure on Tehran to agree to its terms - a move that has infuriated Iran.

Israeli and US forces began massive air strikes on Iran on 28 February. A ceasefire in the Iran war came into effect last month.