The premier raised discriminatory legislation affecting same-sex couples, women and girls, in an address to Commonwealth leaders in London.
"I am all too aware that these laws were often put in place by my own country. They were wrong then, and they are wrong now," she said in a speech to the biennial Commonwealth Heads of Government Meeting (CHOGM).
"As the UK's prime minister, I deeply regret both the fact that such laws were introduced, and the legacy of discrimination, violence and even death that persists today," she added.
Same-sex marriage is legal in Britain, but many countries have held onto legislation imposed by their former colonial rulers.
Living in Pakistan as a homosexual woman
Globally 72 countries criminalise same-sex relationships, according to a 2017 report by the International Lesbian, Gay, Bisexual, Trans and Intersex Association.
The organisation pinpoints British colonial-era legislation still being used in Commonwealth members including Uganda, Malaysia and Singapore.
Britain's premier said her government would back plans to scrap such laws: "The UK stands ready to support any Commonwealth member wanting to reform outdated legislation that makes such discrimination possible."
May's speech was met with applause, but her criticism of other countries' laws could cause a further rupture to the summit which has already been hit with a scandal over emigres to Britain.
The prime minister apologised to Caribbean leaders after her government threatened to deport some of the hundreds of thousands of people who moved to Britain from the region in the 1950s and 1960s.
Those who did not get their papers in order are now being treated as illegal as part of the government's crackdown.
But following a backlash May has written to each of the Caribbean countries affected outlining how Britain intends to rectify the situation.
The row has cast a shadow over the summit, which the UK government had hoped would be an opportunity to promote trade with Commonwealth countries, ahead of Britain leaving the European Union next year.
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