A spokesperson for the prime minister said the government "regrets” President Donald Trump’s move to restore economic restrictions lifted in 2015 when Tehran signed up to a nuclear deal.
He said the international agreement continues to makes the world a safer place, and that British firms should “take advantage” of commercial opportunities with Iran.
He also explained work is being done to protect businesses from the knock-on impact of secondary sanctions.
“We regret the re-imposition of sanctions by the US,” he said.
“We continue to believe that the Iran nuclear deal makes the world a safer place and our position remains that as long as Iran continues to meet its obligations under the deal by respecting strict limits on its nuclear activity we will be committed to it too."
Ms May, France’s Emmanuel Macron and Germany’s Angela Merkel said in May that they remained firmly committed to the Iran nuclear deal after Mr Trump announced he was pulling the US out.
The prime minister told the US president the UK was sticking with the agreement in a telephone call at the time.
Under the Joint Comprehensive Plan of Action, Iran agreed to scale back key elements of its nuclear energy programme associated with the development of a nuclear weapon in return for the easing of economic sanctions.
Mr Trump has insisted the deal that was struck three years ago under the Obama administration was not tough enough on Iran.
The US sanctions are aimed at the Iranian oil industry. US Secretary of State Mike Pompeo said on Monday that 20 nations have cut their oil imports from the Iran, and that the country’s exports have fallen by more than a million barrels a day.
“We are in the war situation,” he said on Monday. “We are in the economic war situation. We are confronting a bullying enemy. We have to stand to win.”
At a meeting of economists broadcast live on state TV, Mr Rouhani vowed to “continue to sell our oil… to break sanctions”.
Additional reporting by agencies
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