Theresa May has used a major speech in the US to warn Donald Trump and his Republican party to “beware” of Vladimir Putin.

Invoking the spirit of the Cold War, she called on the US and the UK to engage with the Kremlin “from a position of strength” and warned about the possible “eclipse of the West” if they failed.

But the Prime Minister also said the days in which the West seek to "remake the world in our own image are over", citing the wars in Iraq and Afghanistan and leaving others to remember David Cameron's ill-fated foray into Libya.

She also pledged support to Mr Trump in the fight against Isis and “Iran’s aggressive efforts to build an arc of influence from Tehran through to the Mediterranean”. But she backed the nuclear deal the new President has threatened to tear up.

The Prime Minister was speaking on foreign policy to US congressmen and women who had gathered at the Republican Retreat – with the party now controlling both Houses of the US legislature, their support will be critical to Ms May’s drive for a new “special relationship”.

She said that the end of the Cold War had seen countries with little tradition of democracy, liberty and human rights – notably China and Russia grow “more assertive in world affairs”.

Ms May went on: “When it comes to Russia, as so often it is wise to turn to the example of President Reagan who, during negotiations with his opposite number Mikhail Gorbachev, used to abide by the adage ‘trust but verify’.

“With President Putin, my advice is to ‘engage but beware’.”

Vladimir Putin says Donald Trump didn't use prostitutes because he's met so many beautiful women

The comments are likely to anger the Kremlin, which has accused Foreign Secretary Boris Johnson of seeking to start a new Cold War and drive a wedge between Moscow and Washington.

Ms May went on: “There is nothing inevitable about conflict between Russia and the West. And nothing unavoidable about retreating to the days of the Cold War. But we should engage with Russia from a position of strength.”

She then sought to draw a line under the policies of her and Mr Trump's predecessors, she said: "This cannot mean a return to the failed policies of the past.

"The days of Britain and America intervening in sovereign countries in an attempt to remake the world in our own image are over. But nor can we afford to stand idly by when the threat is real and when it is in our own interests to intervene. We must be strong, smart and hard-headed. And we must demonstrate the resolve necessary to stand up for our interests."

The controversial orders Donald Trump has already issued Show all 9 1 /9 The controversial orders Donald Trump has already issued The controversial orders Donald Trump has already issued Trump and the media White House Press Secretary Sean Spicer takes questions during the daily press briefing Getty Images The controversial orders Donald Trump has already issued Trump and the Trans-Pacific Partnership Union leaders applaud US President Donald Trump for signing an executive order withdrawing the US from the Trans-Pacific Partnership negotiations during a meeting in the Roosevelt Room of the White House in Washington DC. Mr Trump issued a presidential memorandum in January announcing that the US would withdraw from the trade deal Getty The controversial orders Donald Trump has already issued Trump and the Mexico wall A US Border Patrol vehicle sits waiting for illegal immigrants at a fence opening near the US-Mexico border near McAllen, Texas. The number of incoming immigrants has surged ahead of the upcoming Presidential inauguration of Donald Trump, who has pledged to build a wall along the US-Mexico border. A signature campaign promise, Mr Trump outlined his intention to build a border wall on the US-Mexico border days after taking office Getty Images The controversial orders Donald Trump has already issued Trump and abortion US President Donald Trump signs an executive order as Chief of Staff Reince Priebus looks on in the Oval Office of the White House. Mr Trump reinstated a ban on American financial aide being granted to non-governmental organizations that provide abortion counseling, provide abortion referrals, or advocate for abortion access outside of the United States Getty Images The controversial orders Donald Trump has already issued Trump and the Dakota Access pipeline Opponents of the Keystone XL and Dakota Access pipelines hold a rally as they protest US President Donald Trump's executive orders advancing their construction, at Columbus Circle in New York. US President Donald Trump signed executive orders reviving the construction of two controversial oil pipelines, but said the projects would be subject to renegotiation Getty Images The controversial orders Donald Trump has already issued Trump and 'Obamacare' Nancy Pelosi who is the minority leader of the House of Representatives speaks beside House Democrats at an event to protect the Affordable Care Act in Los Angeles, California. US President Donald Trump's effort to make good on his campaign promise to repeal and replace the healthcare law failed when Republicans failed to get enough votes. Mr Trump has promised to revisit the matter Getty Images The controversial orders Donald Trump has already issued Donald Trump and 'sanctuary cities' US President Donald Trump signed an executive order in January threatening to pull funding for so-called "sanctuary cities" if they do not comply with federal immigration law AP The controversial orders Donald Trump has already issued Trump and the travel ban US President Donald Trump has attempted twice to restrict travel into the United States from several predominantly Muslim countries. The first attempt, in February, was met with swift opposition from protesters who flocked to airports around the country. That travel ban was later blocked by the Ninth Circuit Court of Appeals. The second ban was blocked by a federal judge a day before it was scheduled to be implemented in mid-March SANDY HUFFAKER/AFP/Getty Images The controversial orders Donald Trump has already issued Trump and climate change US President Donald Trump sought to dismantle several of his predecessor's actions on climate change in March. His order instructed the Environmental Protection Agency to reevaluate the Clean Power Plan, which would cap power plant emissions Shannon Stapleton/Reuters

Ms May then said that the financial crisis, its fall out, a loss of confidence in the West following 9/11, the military interventions in Iraq and Afghanistan and terrorist attacks had “led many to fear that, in this century, we will experience the eclipse of the West”.

But she argued that it is not inevitable and that as other countries grew stronger they may also embrace Western values.

While she said the UK would stand with the US in the fight against Islamic State she argued that “we must employ all of the diplomatic means at our disposal” to defeat it, seeking to temper the more hawkish rhetoric of the President.

She added: “Progress on this issue would also help to secure another of this nation’s priorities – to reduce Iran’s malign influence in the Middle East.

“This is a priority for the UK too as we support our allies in the Gulf States to push back against Iran’s aggressive efforts to build an arc of influence from Tehran through to the Mediterranean.”