In a statement to the House of Commons, Mrs May made clear that the UK intends to honour the commitments it signed up to at the meeting in Canada, even after the US president dramatically repudiated them in an end-of-summit tweet.
While making no direct criticism of Mr Trump, Mrs May acknowledged that the summit had been “difficult” and told MPs she had expressed her “deep disappointment” at the “unjustified” imposition of tariffs on American imports of European steel and aluminium.
She left no doubt that EU nations will impose counter-measures on US goods in response, but cautioned against tit-for-tat retaliation which might lead to a trade war.
Mrs May pointedly voiced her support for the rules-based international order which some commentators have accused Mr Trump of putting at risk.
“This was a difficult summit, with at times some very candid discussions,” Mrs May told MPs. “But the conclusion I draw is that it is only through continued dialogue that we can find ways to work together to resolve the challenges we face.
“The countries round the G7 table have been pillars of the rules-based international order which has benefited all our citizens and, I believe, the world as a whole.
“The United Kingdom, with our allies and partners, will continue to play our part in promoting that order to the benefit of all.”
Shortly after the summit ended on Saturday, Mr Trump used Twitter to announce that he was ordering officials not to endorse the G7 communique agreed hours earlier by the US, UK, Canada, France, Germany, Italy and Japan.
His tweet, shortly after leaving Charlevoix in Quebec, came in response to what he claimed were “false statements” by the summit host, Canadian premier Justin Trudeau.
But Theresa May’s official spokesman left no doubt that the Prime Minister continues to regard the communique as binding on the US.
“The communique was agreed by all parties who attended G7,” the spokesman told a Westminster press briefing.
“We fully intend to honour it. We would hope that the US would similarly honour the commitments that they have made.”
Mrs May later said in her statement: “The UK fully intends to honour the commitments we have made.”
European Commission spokesman Margaritis Schinas used a Latin term “Pacta sunt servanda” - or “agreements must be kept” - as he made clear that Brussels expects Washington to honour its commitments.
Mr Schinas told a Brussels press conference: “The EU stands fully behind the G7 communique agreed in Charlevoix.
“The European Union will continue to stand up for an international, rules-based, multilateral system.
“The European Commission sticks to the final declaration communique and will take all the necessary action at our level to achieve and promote the objectives set therein.
“For us, pacta sunt servanda. After two days of intense negotiations and an even longer preparatory process at sherpa level, the text reflects the values and policies that the EU stands for and that we will continue together with our partners to defend.”
During the summit, Mr Trump accused other states of “robbing” his country through their trade policies and proposed scrapping tariffs across the G7.
In his tweet after departing Charlevoix, he wrote: “Based on Justin’s false statements at his news conference, and the fact that Canada is charging massive Tariffs to our U.S. farmers, workers and companies, I have instructed our U.S. Reps not to endorse the Communique as we look at Tariffs on automobiles flooding the U.S. Market!”