Britain has "no intention of walking away" from the Iran nuclear deal despite the United States pulling out, Foreign Secretary Boris Johnson says.
Mr Johnson told MPs the UK would "strive to preserve the gains" made by the international agreement.
The 2015 deal curbed Iran's nuclear activities in return for the lifting of UN, US and EU sanctions.
US President Donald Trump announced on Tuesday he will pull out, describing it as "defective at its core".
Labour accused the president of a "reckless, senseless and immoral act of diplomatic sabotage".
But some Conservative MPs - including former defence secretary Sir Michael Fallon - backed Mr Trump's stance.
Other signatories to the agreement - the UK, France, China, Russia and Germany - say they remain committed to it.
Iran has said it will try to salvage the agreement, but would restart uranium enrichment if it could not.
Mr Johnson - who had travelled to the United States in a last-minute attempt to persuade the Trump administration not to ditch the deal - told MPs the responsibility was now on the president to set out how he plans to secure a new settlement.
"Britain stands ready to support that task, but in the meantime we will strive to preserve the gains made by the [agreement]", he added.
The foreign secretary said while the UK shared US concerns about Iran, the "painfully negotiated" agreement was effective and had increased the amount of time it would take Tehran to develop nuclear weapons.
A watchdog has reported nine times that Iran had complied with the terms of the agreement, he added.
Mr Johnson also said the government would do its utmost to protect UK commercial interests in Iran from US sanctions.
Sir Michael Fallon - who was UK defence secretary when the deal was signed - said the US president was right in his criticism of the "rather flimsy agreement" which he said "should never have been called comprehensive".
"Far from constraining Iranian behaviour, it has enabled the Iranian regime to use its new financial freedom to interfere in Syria, in Iraq, above all in Yemen and to sponsor Houthi attacks on our friends in Saudi Arabia," he said.
Mr Johnson said he did "not recall him making these points" at the time and disagreed with his views.
Another former minister, Robert Halfon, said the UK should support the US instead of "appeasing" Iran, and Andrew Percy condemned Iran's "increasingly malign and dangerous influence".
After speaking to each other on Tuesday evening, Mrs May, German Chancellor Angela Merkel and French President Emmanuel Macron made clear they would not let the agreement - officially known as the Joint Comprehensive Plan of Action (JCPoA) - collapse.
In a joint statement, they said they regretted President Trump's decision.
"Our governments remain committed to ensuring the agreement is upheld, and will work with all the remaining parties to the deal to ensure this remains the case including through ensuring the continuing economic benefits to the Iranian people that are linked to the agreement," they wrote.
"After engaging with the US Administration in a thorough manner over the past months, we call on the US to do everything possible to preserve the gains for nuclear non-proliferation brought about by the JCPoA, by allowing for a continued enforcement of its main elements."
The UK's Middle East Minister Alistair Burt said the UK would be seeking to "de-escalate" the situation, "no matter how difficult that is in a tricky region".
Why did the US withdraw?
In his address on Tuesday, President Trump called the nuclear accord - or Joint Comprehensive Plan of Action (JCPOA) as it is formally known - a "horrible, one-sided deal that should have never, ever been made".
He said he would work to find a "real, comprehensive, and lasting" deal that tackled not only the Iranian nuclear programme but its ballistic missile tests and activities across the Middle East.
Mr Trump also said he would reimpose economic sanctions that were waived when the deal was signed in 2015.
The US Treasury said the sanctions would target industries mentioned in the deal, including Iran's oil sector, aircraft manufacturers exporting to Iran and Iranian government attempts to buy US dollar banknotes.
Major European and US companies are likely to be hit. Some exemptions are due to be negotiated but it is not yet clear what.
US National Security Adviser John Bolton is reported as saying that European companies doing business in Iran will have to stop doing so within six months or face US sanctions.
Failure of diplomacy
Analysis by the BBC's diplomatic correspondent James Landale
Donald Trump's decision to withdraw the US from the Iran nuclear deal represents a failure of British and European diplomacy. They were unable to persuade the US president to change his mind.
But it also marks the start of the next and perhaps harder task of trying to hold what is left of the agreement together. All three countries have promised to stay in the deal, known by its acronym the JCPoA.
All three countries have promised to work with the remaining signatories to uphold the agreement. The key question will be how far the UK and other European countries are ready and able to go to protect their banks and firms from US sanctions if they do business with Iran.
Labour: Trump is a bully
The shadow foreign secretary Emily Thornberry said Washington's decision risked plunging the Middle East into "deeper destruction, chaos and conflict".
"If the nuclear deal is torn up, we not only destroy that platform for future progress, we risk triggering a rapid nuclear arms race in the Middle East, we risk the hardline theocrats seizing all the reins of power in Tehran, and we risk the descent into an unimaginable conflict with Iran," she said.
Ms Thornberry told the BBC she would have taken a "different approach" towards Mr Trump, describing the US president as a "bully" that she would "stand up to".
"Boris Johnson was complacent, and what he did was too little too late," she said, warning of the US "trampling on our business" with sanctions on UK firms that trade in Iran.
The SNP's Stephen Gethins said President Trump's "deeply reckless" move had undermined the importance of the democratic process.
Liberal Democrat leader Sir Vince Cable said the government had "discovered the limits of sycophancy" in dealing with the US president, calling for safeguards for industry affected by US sanctions.