She said criminalising same-sex relationships among Commonwealth nations is wrong.
May made her plea while speaking at the first joint forum of the 25th Commonwealth Heads of Government Meetings (CHOGM) in Westminster on Tuesday, April 17, 2018.
She said criminalising same-sex relationships in Commonwealth nations is wrong and appealed to leaders to abolish them even though those laws were originally made in the United Kingdom.
She said, "Across the world, discriminatory laws made many years ago continue to affect the lives of many people, criminalising same-sex relations and failing to protect women and girls.
"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. 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.
"As a family of nations we must respect one another's cultures and traditions. But we must do so in a manner consistent with our common value of equality, a value that is clearly stated in the Commonwealth charter.
"Recent years have brought welcome progress. The three nations that have most recently decriminalised same-sex relationships are all Commonwealth members, and since the heads of government last met the Commonwealth has agreed to accredit its first organisation for lesbian, gay, bisexual and transgender people.
"Yet there remains much to do. Nobody should face persecution or discrimination because of who they are or who they love. And the UK stands ready to support any Commonwealth member wanting to reform outdated legislation that makes such discrimination possible."
May also charged Commonwealth leaders to work together on other global issues such as free and fair trade, climate change, youth unemployment, quality all-inclusive education, global security, as well as tackling malaria and modern slavery.
The PM had met with President Muhammadu Buhari at Downing Street, London on Monday, April 16, to discuss Nigeria-British relations ahead of the meetings.
While speaking to May during Monday's meeting, President Buhari focused on the three main agenda of his administration - security, economy and fight against corruption. He also urged British companies to invest more in Nigeria.
He said, "British companies like Unilever, Cadbury, and many others have stood with Nigeria through thick and thin. Even when we fought a Civil War, they never left.
"But like Oliver Twist, we ask for more investments. We are encouraging more British companies to come to Nigeria. We appreciate the support you have given in training and equipping our military, particularly in the war against insurgency, but we want to also continue to work with you on trade and investment."
In 2014, then-president, Goodluck Jonathan, signed the Same-Sex Marriage (Prohibition) Bill (SSMPA) into law. At that time, existing legislation already criminalised consensual same-sex activities in the country.
The law forbids any cohabitation between same-sex sexual partners and bans any 'public show of same sex amorous relationship'. The law also prohibits Nigerians from registering, operating, or participating in gay clubs, societies and organisations, or supporting such activities.
Punishment for violations of the provisions in the law range between 10 to 14 years imprisonment.
The law has been criticised for violating fundamental human rights and endorsing physical violence, aggression, arbitrary detention and harassment of lesbian, gay, bisexual, and transgender (LGBT) people in the country.