Donald Trump has offered Iran direct talks, saying its leaders should “call me” and suggested the US would help revive the country’s economy as long as Iran did not acquire nuclear weapons.

The impromptu offer by the US president, if serious, represents a dramatic lowering of the bar set by his administration for lifting extensive sanctions, including an oil embargo. Iran is already party to a 2015 agreement that strictly limits its nuclear programme and places it under close scrutiny. Trump withdrew the US from the Obama-era treaty a year ago.

“What I’d like to see with Iran, I’d like to see them call me,” Trump said. He pointed out the Iranian economy was in a shambles as a result of the pressure from the US.

“What they should be doing is calling me up, sitting down and we can make a deal, a fair deal,” Trump said. “We just don’t want them to have nuclear weapons. It’s not too much to ask. And we would help put them back into great shape.”

The Trump administration has previously insisted Iran would have to fulfil a list of 12 wide-ranging conditions, including non-intervention in Syria, Yemen and Iraq, in order for sanctions to be lifted. Trump’s remarks suggested that a new deal on the nuclear programme would be enough.

The new Iranian ambassador to the UN, Majid Takht Ravanchi, immediately responded by saying Iran had no interest in developing nuclear weapons.

“The first question that he has to answer is why he left the negotiating table because we were talking to all participants of the nuclear deal, including the US,” Ravanchi told NBC News. “So all of a sudden he decided to leave the negotiating table … What is the guarantee that he will not renege again on the future talks between Iran and the US?”

In his remarks, Trump accused former secretary of state John Kerry of telling Iran not to negotiate with his administration, which he claimed was a violation of the Logan Act, which bans private individuals from negotiating with foreign states.

The allegation was denied by a spokesman for Kerry’s office, who told CNN: “Everything President Trump said today is simply wrong, end of story. He’s wrong about the facts, wrong about the law, and sadly he’s been wrong about how to use diplomacy to keep America safe.”

Asked why the US had sent an aircraft carrier to the Middle East in response to allegedly menacing behaviour by Iran, Trump said: “They were threatening and we have information that you don’t want to know about. They were very threatening and we just want to have … great security for this country and for a lot of other places.”

And on the question of whether there could be a military confrontation, he replied: “I guess you could say that always, right? I don’t want to say no, but hopefully that won’t happen. We have one of the most powerful ships in the world that is loaded up and we don’t want to do anything.”

Trump’s national security adviser, John Bolton, has been pushing an aggressive stance towards Iran and made the announcement of the military deployments, but the Washington Post reported on Wednesday that Bolton has irritated Trump over his involvement in a failed effort to oust the Venezuelan leader, Nicolás Maduro.

“John .. has strong views on things, but that’s OK. I actually temper John, which is pretty amazing, isn’t it?” Trump joked to reporters on Thursday.

Facebook Twitter Pinterest The Iranian president, Hassan Rouhani (right), inspects the country’s nuclear technology. Photograph: Iranian Presidency Office Handout/EPA

The president made his remarks at a time of rising tensions over the 2015 nuclear deal. Iran announced its intention to violate elements of the agreement on Wednesday, in response to what it said was the failure of the US and other state parties to meet their side of the bargain by relaxing sanctions.

The EU and the foreign ministers of Germany, France and Britain have said they would not accept ultimatums from Iran over the nuclear deal, but admitted to sharp differences with the US over how to change Tehran’s behaviour.

The European leaders, increasingly hampered by the US’s determination to weaken Iran, also said they were still committed to the deal and did not at this stage see threats from Tehran to loosen its obligations as being in breach of the agreement.

On Wednesday the Iranian president, Hassan Rouhani, reduced Iran’s obligations under the deal and said his country would take further steps in 60 days on uranium enrichment if the EU did not do more to help the Iranian oil and banking sector. In its initial step, Tehran said it would no longer limit its stocks of heavy water or low-enriched uranium.

The EU said in response: “We reject any ultimatums and we will assess Iran’s compliance on the basis of Iran’s performance regarding its nuclear-related commitments under the joint comprehensive plan of action (JCPOA) and the treaty on the non-proliferation of nuclear weapons.”

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In a tweeted response on Thursday, the Iranian foreign minister, Mohammad Javad Zarif, derided the EU statement.

“The US has bullied Europe – and rest of world – for a year and EU can only express ‘regret’,” Zarif said. “Instead of demanding that Iran unilaterally abide by a multilateral accord, EU should uphold obligations – [including] normalization of economic ties.”

The JCPOA is the technical term for the deal signed in 2015 by Iran, Russia, China, the US and three EU states, France, Britain and Germany.

The EU said it regretted the reimposition of sanctions by the US after it withdrew from the nuclear deal last year and that the EU remained committed to preserving and fully implementing the deal, including helping the Iranian people enjoy the benefits of sanctions relief.

The US laid on further sanctions on Wednesday, mainly focused on the Iranian iron, steel, aluminium and copper industry and apparently designed to push Iranian manufacturing deeper into recession, potentially provoking a rift between blue-collar workers and the government.

Iran wanted to bring its nuclear deal with world powers “back on track” after the US’s unilateral withdrawal, Behrouz Kamalvandi, a spokesman for the Atomic Energy Organization of Iran, said.

Since pulling out of the deal, Trump has been trying to isolate Iran economically and force Europe to back away from any trading contact, save some humanitarian supplies.

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The US “maximum pressure campaign” is formally designed to press Iran to renegotiate perceived weaknesses in the deal, but Washington’s critics claim the true aim is to bring the Iranian economy to its knees and provoke a revolution.

Tehran is frustrated that Europe says it opposes US actions but seems at best slow in devising a financial mechanism or legal entities that would protect those European companies that wish to trade with Iran.

With EU leaders gathering for an informal summit in the Romanian town of Sibiu, the French president, Emmanuel Macron, appealed for calm on all sides, saying Europe must work to convince Iran to stick with the deal. “We must not get jumpy or fall into escalation,” Macron said.