May heaped praise upon Republicans for their election victories in November, saying it was an "honor" to address them as "dawn breaks on a new era of American renewal."
But she went on to deliver some tough messages to the new administration of US President Donald Trump, calling on the US not to abandon the Iran nuclear deal, to defend Russia's neighboring states and to support international institutions such as NATO.
May will become the first foreign leader to meet President Trump at the White House on Friday, and the pair will hold a joint news conference later. Her speech on Thursday, to GOP leaders gathered in Philadelphia for their annual retreat, was clearly aimed at shaping the new President's world view.
May signaled a retreat from interventionist policies of previous UK and US leaders like Tony Blair and George W. Bush, saying that a renewed UK-US partnership could not repeat 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," she said.
Praise for Trump
May went out of her way to congratulate the Republicans on their election wins.
"Because of this, because of what you have done together, because of that great victory you have won, America can be stronger, greater, and more confident in the years ahead," she said to applause. "And a newly emboldened, confident America is good for the world."
She praised the stunning win of Trump, saying it came in defiance of "pundits and polls" and echoed the hopes of working Americans.
May reminded the audience that like them she, too, is a conservative and someone who believes in putting power in the "hands of the people."
But she went on to urge the US not to abandon its leadership role in the world, saying that the historic partnership with the UK not only helped win wars and overcome trouble, "it made the modern world."
She added that the two nations have a responsibility to lead. "Because when others step up as we step back, it is bad for America, for Britain and the world," she said.
Calls for reform of NATO and UN
May was careful to acknowledge the suspicions held by Trump about multinational institutions such as NATO, the UN and the International Monetary Fund. "Some of these organizations are in need of reform and renewal to make them relevant to our needs today," she said.
In a nod to Trump's desire to put American interests first, May stressed the importance of the "nation state".
But later she said that to deal with modern threats of ISIS and other bad actors, the US and UK need to "turn toward those multinational institutions like the UN and NATO that encourage international cooperation and partnership."
Russia and Iran
May gave a cautious endorsement of Trump's desire to rebuild relations with Russia, urging the US to tread carefully.
"With President Putin, my advice is to engage, but beware," she said. "We should engage with Russia from a position of strength and build the relationship, systems, and processes that make cooperation more likely than conflict."
She made it clear that Britain viewed Russia's annexation of Crimea from Ukraine as "illegal" -- Trump has been equivocal on the issue -- and said Russia's neighboring states required assurance that their security was not in question.
With respect to Iran, May called for a push-back against Tehran's "aggressive efforts" to build its influence through the Middle East to Europe. She acknowledged that the nuclear agreement with Iran was "controversial" and required tough policing, but said it was a vital deal for regional security and was working.
That message was heard in silence -- congressional Republicans have long opposed the Iran deal, struck by the Obama administration.
Quentin Peel -- a fellow with the Europe Programme at Chatham House, an independent policy institute based in London -- called May's remarks a forceful speech.
"I was expecting her to be a little more diplomatic. She was very clear on certain things on which Donald Trump doesn't look so clear," he told CNN
May said she was delighted that the Trump administration had made a trade agreement between the United States and the UK a priority.
"It will take detailed work, but we welcome your openness to these discussions and hope we can make progress so that the new global Britain that emerges after Brexit is even better equipped to take its place confidently in the world," she said, referring to Britain's exit from the European Union.
According to May, the UK is the fifth-leading importer of US goods and the US is the largest market for UK overseas investments. It was in the national interest of both countries to strike a good deal, she said. May's remarks were greeted with warm applause, suggesting a openness amongst Republicans to May's overtures on trade.