Iran has offered a deal with the US in which it would formally and permanently accept enhanced inspections of its nuclear programme, in return for the permanent lifting of US sanctions.

The offer was made by the Iranian foreign minister, Mohammad Javad Zarif, on a visit to New York. But it is unlikely to be warmly received by the Trump administration, which is currently demanding Iran make a range of sweeping concessions, including cessation of uranium enrichment and support for proxies and allies in the region.

Zarif insisted, however, that his offer was “a substantial move”.

“It’s not about photo ops. We are interested in substance,” he told reporters at the Iranian mission to the UN in New York on Thursday. “There are other substantial moves that can be made.”

He said: “If they [the Trump administration] are putting their money where their mouth is, they are going to do it. They don’t need a photo op. They don’t need a two-page document with a big signature.”

Iran has faced an steadily tightening US-driven oil embargo and severe banking sanctions since May last year, when Donald Trump withdrew the US from the 2015 multilateral nuclear deal with Iran known as the Joint Comprehensive Programme of Action (JCPOA).

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The embargo has triggered a standoff in the Gulf that has escalated dramatically in recent months:on Thursday, Trump said a US warship, the USS Boxer, had shot down an Iranian drone that had come within a kilometre of the vessel.

“The drone was immediately destroyed,” the president said. “This is the latest of many provocative and hostile actions by Iran against vessels operating in international waters. The United States reserves the right to defend our personnel, facilities, and interests.”

Earlier in the day, Iran said it had seized a foreign-owned vessel suspected of being used for oil smuggling out of Iran.

Zarif dismissed the seizure as a routine marine policing matter.

He said: “It’s not a tanker. It’s a small ship carrying a million litres, not a million barrels, of oil. We do it every other day. These are people who are smuggling our fuel. This is … one of the things that we do in the Persian Gulf, because of the heavy subsidies that we provide for our own fuel products.”

Zarif credited Trump with “prudence” for calling off missile attacks last month in reprisal for the downing of a US surveillance drone, and said that gave him confidence that diplomatic progress is possible.

He said: “I believe we were few minutes away from a war. Prudence prevailed and we’re not fighting. So that gives reason for us to be optimists. If we work, if we are serious, then we can find a way forward.”

I believe we were few minutes away from a war. Prudence prevailed. So that gives reason for us to be optimists Mohammad Javad Zarif

Iran’s supreme leader, Ali Khamenei, has rebuffed overtures for direct talks with Trump, citing US bad faith over the JCPOA, but Zarif signaled on Thursday that Iran was willing to do a deal that did not necessary involve the US returning to the JCPOA, Tehran’s official position until now.

Zarif noted that in 2023, under the JCPOA, Iran’s parliament, the Majlis, was supposed to ratify the Additional Protocol of the International Atomic Energy Agency (IAEA), a voluntary agreement that allows IAEA inspectors extensive access in Iran to ensure the country does not have a covert nuclear weapons programme. As part of the JCPOA, Iran already observes the Additional Protocol. Ratification by the Majlis would make it a more permanent commitment.

At the same time, under the JCPOA, the US Congress was due to lift sanctions on Iran.

Zarif proposed that the Iran and US take those steps immediately.

“If Trump wants more for more, we can ratify the Additional Protocol and he can lift the sanctions he set,” Zarif said. “He has said that he will take any measure to Congress – fine. Lift the sanctions and you’ll have the Additional Protocol sooner than 2023.”

The state department has yet to respond to Zarif’s proposal, but its official position is that Iran has to fulfil a wide-ranging list of 12 conditions, including curtailing its involvement in regional conflicts, in order to win sanctions relief. Iran has rejected those demands.

Zarif also denounced the seizure of a tanker carrying Iranian oil by UK forces in Gibraltar, which said was carried out on behalf of the US.

“That’s a violation of international law,” he said.

The UK has said the tanker, the Grace 1, would be released if Iran could demonstrate it was not heading for Syria, which is banned by the EU. Zarif said it was not bound for Syria but he could not specify who the customer was, as the buyer would consequently be subject to US sanctions.

He said: “We won’t tell you, because if we told you where it was going, next time you wouldn’t be able to sell our oil. We can’t be transparent. We told you it wasn’t going going to Syria – but the rest is none of your business. Because if we told you it would be less one less outlet to buy it to get money to feed our people.”

Zarif also shrugged off a report that Senator Rand Paul was seeking to become a secret emissary between Trump and the Iranian leadership, but would not confirm or deny he would be meeting Paul in his capacity as a member of Congress on his current visit to the US.

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“I don’t deal with [secret] emissaries,” the foreign minister said. He added: “I doubt that anybody will be designated as an emissary by President Trump.”

He said the report in Politico that Paul, a libertarian anti-war Republican, could carry out secret talks was “overblown”

“This is media stuff. I mean, these may be good for a spy movie,” Zarif said. But he also said: “I’d meet with members of Congress in their own personal capacity as influential members of American society and representatives of American people.”