Mrs May reserved special praise for GB stars Laura Trott, Mo Farah, Max Whitlock, Alistair and Jonny Brownlee and teenage gymnast Amy Tinkler as the Olympics drew to a close.
She said: “For the past fortnight, the people of the United Kingdom have been filled with pride as we’ve watched our Olympians take victory in so many sports with power, grace and control.
“In every discipline and at every stage, Team GB have shown the world what we’re made of: determination, dignity and true sportsmanship.
“I have been taking every opportunity to watch these amazing Olympics, keeping up with the team’s brilliant progress.
“Rio 2016 will be remembered as a history-making Olympics for Britain, one where we took more medals than we have ever done at an overseas Games.”