Donald Trump has claimed he has no “exit strategy” if the US goes to war with Iran, the latest sabre-rattling from the US president as tensions between the two countries continues to grow.

On a day that saw Mr Trump threaten to obliterate Iran if it attacked any US assets, and Tehran vowed to respond if another US drone were to breach its airspace, the president nevertheless left open the door for talks. He said Iran should inform the US when it was ready to negotiate.

At the same time, he also suggested that military conflict between the two countries was a genuine possibility.

Asked in the White House – where he was signing an unrelated executive order – if he had an “exit strategy” if the US were to go to war with Iran, he said: “You’re not going to need an exit strategy. I don’t do exit strategies.”

At another photo opportunity with the media, the president was asked what message he had for Iran’s leaders.

Tensions high as Trump approves new Iran sanctions: In pictures Show all 17 1 /17 Tensions high as Trump approves new Iran sanctions: In pictures Tensions high as Trump approves new Iran sanctions: In pictures Iran claims that in this picture released by Iran state TV, their surface-to-air missile is seen as it shoots down a US surveillance drone EPA Tensions high as Trump approves new Iran sanctions: In pictures This photo shows US RQ-4A Global Hawk unmanned surveillance drone. A drone of this model was shot down by Iran on Thursday 21 June AFP/Getty Tensions high as Trump approves new Iran sanctions: In pictures An oil tanker is on fire after it was subject to a suspected attacked at the Gulf of Oman on June 13. The US has blamed Iran for the attack Reuters Tensions high as Trump approves new Iran sanctions: In pictures Iran claims that in this picture released by Iran state TV, debris from the downed US drone is seen after it was recovered from Iranian waters AFP/Getty Tensions high as Trump approves new Iran sanctions: In pictures Smoke billows from an oil tanker after it was subject to a suspected attacked at the Gulf of Oman on June 13 Reuters Tensions high as Trump approves new Iran sanctions: In pictures US President Trump holds up a signed executive order to increase sanctions on Iran on 24 June AP Tensions high as Trump approves new Iran sanctions: In pictures Iranian President Rouhani stated in a televised address that the White House is "afflicted by mental retardation" following the increase in sanctions on 25 June EPA Tensions high as Trump approves new Iran sanctions: In pictures An Iranian navy boat tackles the fire on the Norwegian owned Front Altair oil tanker after it was hit in a suspected attack AFP/Getty Tensions high as Trump approves new Iran sanctions: In pictures Iran claims that in this picture released by Iran state TV, debris from the downed US drone is seen after it was recovered from Iranian waters AFP/Getty Tensions high as Trump approves new Iran sanctions: In pictures Smoke billows from an oil tanker after it was subject to a suspected attacked at the Gulf of Oman on June 13 Reuters Tensions high as Trump approves new Iran sanctions: In pictures A screenshot from a video released by the US Department of Defense that the US claims to show Iranian removing an unexploded limpet mine form the hull of the Japan-owned ship that was attacked in the Gulf of Oman on June 13 Getty Tensions high as Trump approves new Iran sanctions: In pictures An item reportedly found on the Japan-owned oil tanker that was attacked on June 13 in the Gulf of Oman AFP/Getty Tensions high as Trump approves new Iran sanctions: In pictures A handout photograph from the US Department of Defense shows a composite material that the US claim was left behind on the hull of the Japan-owned oil tanker following the removal of an unexploded limpet mine Getty Tensions high as Trump approves new Iran sanctions: In pictures A view from the cabin of an Iranian navy boat as it tackles the fire on the Norwegian owned Front Altair oil tanker after it was hit in a suspected attack EPA Tensions high as Trump approves new Iran sanctions: In pictures Release by US government A picture released by U.S. Central Command shows damage to the hull of the oil tanker Kokuka Courageous. The picture suggests that the ship is 'likely' to have been hit by a mine as the US Secretary of State Mike Pompeo moves to blame Iran for the suspected attack Reuters Tensions high as Trump approves new Iran sanctions: In pictures Smoke billows from an oil tanker after it was subject to a suspected attacked at the Gulf of Oman on June 13 Reuters Tensions high as Trump approves new Iran sanctions: In pictures Release by US government A picture released by U.S. Central Command shows damage to the hull of the oil tanker Kokuka Courageous. The pictures suggests that the ship is 'likely' to have been hit by a mine as the US Secretary of State Mike Pompeo moves to blame Iran for the suspected attack EPA

“I’ll tell you what the message is: when they’re ready, let us know,” he said. Asked if he meant when Iran was ready to negotiate, he added: “Ready to do whatever. Doesn’t make a difference. Whatever they want to do, I’m ready.”

The president had started the day with stern threats, delivered on Twitter. Responding to headlines from Iran that said it considered new US sanctions imposed on Monday against the nation’s supreme leader “closing the door of diplomacy”, Mr Trump said Iran’s comments were “ignorant and insulting”.

“Any attack by Iran on anything American will be met with great and overwhelming force,” he wrote. “In some areas, overwhelming will mean obliteration. No more John Kerry & Obama!”

In Iran, president Hassan Rouhani said the sanctions signed by Mr Trump a day earlier, largely symbolic and targeting Ayatollah Ali Khamenei, showed the US was “afflicted by mental retardation”.

“Tehran’s strategic patience does not mean we have fear,” said Mr Rouhani, who runs Iran’s day-to-day affairs while Mr Khamenei is the country’s ultimate authority.

John Oliver blasts Fox News about Iran war comments

Relations between Iran and the US have worsened since Mr Trump last year withdrew Washington from the multi-party Iran Nuclear Deal, that was designed to monitor Tehran’s nuclear industry, while readmitting it to international markets and lifting sanctions.

But when Mr Trump went ahead and unilaterally pulled the US out, something he had vowed to do during the 2016 presidential campaign, he also reimposed a series of stringent sanctions that have targeted Iran’s oil industry and make it difficult for it to trade with other nations.

This, coupled with a propaganda campaign the US launched last year, has had a deeply damaging, but not yet fatal, impact on the nation’s economy. As recently as April of last year, Iran was exporting more than 2.5 million barrels per day of crude oil; this month, the figure has fallen to just 300,000.

Earlier this month, Iran said it was preparing to breach the limit for uranium production agreed as part of the deal signed in 2015, an apparent attempt to try and lever the EU and other signatories to help it counter the impact of US sanctions.

Tensions soared when Iran last week shot down a US drone it claimed was in Iranian airspace, and Mr Trump said he had called off a retaliatory airstrike with minutes to spare as he did not want to kill the 150 people estimated to lose their lives as a result.

The US has insisted the drone was in international airspace, while Iran has produced the coordinates it claims proves it had crossed the line.

In a telephone conversation on Tuesday with French president Emmanuel Macron, Mr Rouhani said Iran was not looking for war. However, he said if the US again violated Iranian airspace Iran would defend itself.

“If the Americans want to violate the waters or airspace of Iran again, Iran’s armed forces have a duty to confront them and they will have a decisive clash,” Mr Rouhani said, according to Iranian media.

During a visit to Israel, Mr Trump’s hawkish national security advisor, John Bolton, said the US was prepared to hold talks if Iran was ready to go beyond the terms of the deal signed in 2015, something most observers believe unlikely to happen.