British Prime Minister Theresa May has said she deeply regrets the UK's role in criminalizing same-sex relations in its former colonies.
The laws were passed under British rule and are still used in 37 of the Commonwealth's 53 member nations.
There is a global trend towards decriminalizing homosexual acts, but some countries, like Nigeria and Uganda, have imposed stricter laws.
At a Commonwealth meeting, Mrs May said laws were "wrong then and wrong now".
Same-sex relations are explicitly banned in 72 countries, according to the International Lesbian, Gay, Bisexual, Trans and Intersex Association (ILGA).
"Nobody should face discrimination and persecution because of who they are or who they love," Mrs May said in London as Commonwealth leaders gather for their summit, which is held every two years.
"The UK stands ready to support any Commonwealth nation wanting to reform outdated legislation that makes such discrimination possible.
"Across the world discriminatory laws made many years ago continue to affect the lives of many people, criminalizing same-sex relations and failing to protect women and girls."
The number of states that criminalize same-sex relations is decreasing annually, with Belize and the Seychelles repealing such laws in 2016.
But in many socially conservative and religious countries in Africa, where homosexuality is a taboo, there has been resistance to calls to decriminalize same-sex relationships.
South Africa, which rejoined the Commonwealth after the end of white-minority rule in 1994, is one of the exceptions.
It has one of the most liberal constitutions in the world, which protects gay rights, and was the first African country to legalize same-sex marriage in 2006.
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