The killing of Qassem Soleimani had created a “very risky situation” in the Middle East, a “dangerous game of chicken” in which both the US and Iran gamble on the other not starting a war, he warned.
Asked if the US president had “miscalculated” in carrying out the airstrike on General Soleimani’s convoy at Baghdad airport, Mr Hunt replied: “Only time will tell.”
The comment came after Mike Pompeo, the US secretary of state, criticised the UK, France and Germany for failing to be “as helpful as I wish that they could be”, by not backing the attack.
Meanwhile, the Foreign Office urged British citizens to avoid all essential travel to Iran and all travel to Iraq, outside the Kurdistan region.
Mr Trump has insisted the killing of General Soleimani was carried out “to stop a war, not to start one”, hailing the end of his “reign of terror”.
But Mr Hunt said: “It’s an increasingly dangerous game of chicken that’s going on at the moment, because both sides have calculated that the other side cannot afford and doesn’t want to go to war
“So they are doing increasingly extreme things – not just the killing of General Soleimani, but the [Iran-backed] bombing of the Saudi oil factory last September is another example of this.”
And he added: “The job that we have to do, as one of the US closest allies, is to use our influence to argue for more consistent US policy.”
Mr Hunt, who was sacked by Boris Johnson, also criticised the failure to even warn the UK about the killing, telling BBC Radio 4’s Today programme: “It is regrettable as one of the US’s closest allies. It’s an important aspect that there are no surprises in that relationship.”
In a statement on Friday, Dominic Raab, the foreign secretary, avoided backing the killing, instead urging “all parties to de-escalate’, saying: “Further conflict is in none of our interests.”
The prime minister has not commented, while on holiday on the private Caribbean island of Mustique. Downing Street has not said when he will return.
Jeremy Corbyn, the outgoing Labour leader, wrote to Mr Johnson calling for an urgent meeting of the privy council to discuss whether the “assassination” had heightened the terror risk to the UK.
“The UK government should urge restraint on the part of both Iran and the US and stand up to the belligerent actions and rhetoric coming from the United States,” Mr Corbyn warned.
The fresh travel advice came as thousands began to gather on the streets of Iraq for the funeral of General Soleimani and as the world awaited Tehran’s threatened response.
Mr Raab said it was issued due to “heightened tensions in the region”, adding: “The first job of any government is to keep British people safe.”