Iran has said it has replied to a US peace proposal, on a day when the month-old ceasefire showed signs of fraying, as drone strikes were reported around the region and Benjamin Netanyahu warned the war was “not over”.

Iranian state media reported that Tehran’s response had been passed to Pakistani mediators. Pakistan confirmed it had been forwarded to Washington.

The semi-official Tasnim news agency, citing an informed source, said on Sunday night that Iran’s proposed text for negotiations underlined the necessity of lifting US sanctions, ending the US naval blockade of the strait of Hormuz after the signing of initial understanding, and an immediate end to the war with guarantees against any renewed attack on the country.

The US president, Donald Trump, responded shortly afterwards by saying: “I have just read the response from Iran’s so-called ‘representatives’. I don’t like it – totally unacceptable.”

The US had presented a peace proposal a week ago, which was reported to consist of a one-page, 14-point memorandum of understanding that would reopen the strait of Hormuz while setting a framework for further talks on Iran’s nuclear programme.

Netanyahu said the war would continue as long as Iran had a stockpile of highly enriched uranium (HEU), which could be used to make nuclear warheads.

“It’s not over, because there’s still nuclear material – enriched uranium – that has to be taken out of Iran. There’s still enrichment sites that have to be dismantled,” the Israeli prime minister told the CBS programme 60 Minutes, according an excerpt published before its broadcast.

Asked how the HEU should be removed, Netanyahu said: “You go in and you take it out,” adding that the best way would be to enter Iran to secure the fissile material as part of an agreement. He said Donald Trump had told him he wants “to go in there”.

In a separate interview, Trump appeared to take a more relaxed view of the HEU stockpile, which the UN nuclear watchdog, the IAEA, says is buried deep under mountains in central Iran. The US president suggested that for the time being, satellite surveillance was sufficient to guarantee no one had access to it.

Trump said on the Full Measure programme: “We’ll get that at some point … We have it surveilled. I did a thing called Space Force, and they are watching that … If anybody got near the place, we will know about it – and we’ll blow them up.”

As he has on numerous occasions since a ceasefire was declared a month ago, Trump said US attacks on Iran could be resumed. He said the US could “go in for two more weeks and do every single target. We have certain targets that we wanted, and we’ve done probably 70% of them, but we have other targets that we could conceivably hit.

“But even if we didn’t do that, you know, that would just be final touches,” he added.

The president is under heavy pressure to maintain the ceasefire, and potentially make a peace deal, before a scheduled visit this week to China, which is pushing for an end to hostilities and the opening of the strait.

Two critical issues that will be at the heart of any future nuclear talks between the US and Iran are the disposal of Iran’s 440kg of HEU enriched to 60% purity – close to weapons grade – and the suspension of uranium enrichment. In an interview on Iranian state media late on Saturday, a military spokesperson said the country’s forces were at “full readiness” to protect the stockpile.

“We considered it possible that they might intend to steal it through infiltration operations or heliborne operations,” Brig Gen Akrami Nia said.

Trump is reported to have been presented with military options for seizing the HEU, but the operation would have required a large number of troops and would have taken weeks.

Iran was responding on Sunday to a US memorandum which was itself a response to an earlier Iranian proposal. That also envisaged the lifting of parallel US and Iranian blockades on the strait, which have been driving up oil prices and stifling the global economy, with an emphasis on the lifting of sanctions and the release of frozen Iranian assets.

The announcement of a new response from Tehran came on a day when the Pakistan-brokered ceasefire, which came into effect on 8 April, showed new signs of strain. The United Arab Emirates and Kuwait reported drone incursions in their airspace on Sunday, and a drone attack started a small fire on a ship on the coast of Qatar.

Another drone strike was reported at a camp used by an Iranian Kurdish rebel group near Erbil in north-eastern Iraq.

Qatar’s defence ministry did not give details of the vessel targeted on Sunday, other than that it had come from Abu Dhabi. The UAE defence ministry said it had shot down the drones which entered its airspace, and which it said were Iranian.

Kuwait’s defence ministry spokesperson said its forces had dealt with drones which entered the country’s airspace early on Sunday, “in accordance with established procedures”, without attributing responsibility for the incursion.

Meanwhile, Iran’s deputy foreign minister warned against a planned French-British effort that aims to support maritime security in the strait after hostilities are over. The French president, Emmanuel Macron, responded by saying it would not be a military deployment but an international mission to secure shipping when conditions allow.

Tensions have flared under the truce as the US and Iran have sought to assert their control of the Hormuz strait. On 4 May, Donald Trump launched what he called Project Freedom, which was supposed to provide a route out of the Gulf for the hundreds of ships trapped by the war.

Iran, which closed the strait after the initial US-Israeli attack on 28 February, responded with attacks on US naval vessels, commercial vessels and oil facilities in the UAE, a close ally of the US and Israel.

Trump called off Project Freedom after 36 hours and the passage of just two US-flagged ships. Saudi Arabia had refused permission for US forces to use its bases and airspace for the operation.

Tehran has insisted that all ships passing through the strait coordinate with its armed forces and pay a $2m (£1.5m) toll. On Sunday, Iranian state media reported that a Panama-flagged vessel bound for Brazil had been allowed to sail through the strait.

Qatar denounced the strike on a ship in its territorial waters as a “serious escalation”. The country’s prime minister, Sheikh Mohammed bin Abdulrahman Al Thani, told Iran’s foreign minister, Abbas Araghchi, that using the strait as a means of exerting pressure would only deepen the crisis, and that freedom of maritime navigation should not be compromised.

Trump has said that the current ceasefire includes Lebanon, and has told Israel to stop the bombing of Hezbollah targets there. Israel has reduced the intensity of its campaign but has continued to carry out strikes.

Lebanon’s health ministry reported that 36 people had been killed and 74 wounded by Israeli strikes on Saturday. Among the casualties were several paramedics wounded in southern Lebanon. The Israeli military said, meanwhile, that it had intercepted Hezbollah drones approaching its troops in the area.