Wes Streeting has criticised Donald Trump’s rhetoric on Iran as “incendiary, provocative and outrageous” and called the failure of US-Iran peace talks “disappointing”, but said the success of future negotiations was necessary “in all of our interests”.

“As ever in diplomacy, you’re failing until you succeed,” the health secretary told Sunday Morning With Trevor Phillips on Sky News. “So while these talks may not have ended in success, that doesn’t mean there isn’t merit in continuing to try.”

A fragile two-week truce announced on Tuesday has been thrown into uncertainty after Washington and Tehran’s 21 hours of negotiations ended without a peace agreement being reached in the early hours of Sunday. The US vice-president, JD Vance, who was in Pakistan for the talks, said Iran’s refusal to commit to not building a nuclear weapon was the reason for the lack of a deal.

Keir Starmer urged both sides to “find a way through” after the failure of the peace talks. The prime minister also called for the ceasefire to continue after a conversation with the Sultan of Oman, Haitham bin Tariq Al Said, on Sunday morning.

Streeting said of the talks: “Clearly when you look at the impact of the war in Iran on this country, on other countries around the world who have no part in this war, it is in all of our interests for there to be a breakthrough and an end to this war.”

He acknowledged it had been a “difficult few months” for the relationship between the UK and the US. He said that disagreements over the Iran war, Greenland and the Chagos Islands, as well as the US president’s unbridled criticism of the UK’s defensive capabilities and personal criticism of the prime minister had “undoubtedly strained” UK-US relations.

But he added: “On so many other things, our interests as the UK and the US are intertwined.

“We are old and close friends, and we’ve got a shared outlook as democratic countries and we’ve got shared security interests.”

Asked about the rhetoric used by Trump, who last week warned Iran that a “whole civilisation will die” if it did not meet his demands, Streeting said many people would have gone to bed “wondering what on earth would happen overnight”.

He added: “Over the course of the last week, President Trump has said some pretty bold – in Yes Minister language – incendiary, provocative, outrageous things on social media. I think we’ve all come to learn that you judge President Trump through what he does, not just what he says.”

He added that ministers had learned to draw a distinction between what the US president said and what he did: “The point I’m making is you have to distinguish between some of the rhetoric, which people might find shocking, and then the reality.”

Britain is to host further talks with a coalition of countries about reopening the strait of Hormuz shipping lanes next week.

The meeting comes after Starmer spoke to Trump about the need for a “practical plan” to get ships going through the area and said he was “fed up” with the effect that Trump’s actions in the Middle East were having on the British public.

Rachel Reeves said again on Sunday that the war in Iran would “come at a cost to British families and businesses”. Writing in the Sunday Times, the chancellor said: “These are not costs I wanted, but they are costs we will have to respond to. As chancellor, I have vowed that my economic approach to this crisis will be both responsive to a changing world and responsible in the national interest.”

Streeting praised the prime minister’s “grit and guts” in declining to support initial US-Israeli strikes on Iran. “There are few former British prime ministers alive today who would have made the same judgment call that Keir made on not joining the war in Iran,” he said.

He called criticism of the move by the former Labour prime minister Tony Blair and others “extraordinary”, adding: “I am glad that we didn’t join this war. Imagine the extent to which we would be in it up to our necks … When the prime minister made that judgment, he got flak from his predecessors. He got flak from people who would happily take his job at the next general election; Kemi Badenoch, Nigel Farage, they have all been proven completely wrong.”