The leader of Ghana since the January last year, Nana Addo Dankwa Akufo-Addo addressed a major meeting of evangelicals in the capital, Accra.
He was quoted by the Ghana News Agency as saying: "Let me assure you that this government has no plans to change the law on same sex marriage.
"We have no authority and we will not seek any authority to do so."
Mr Akufo-Addo was responding to a plea made by the Moderator of the Global Evangelical Church, which claims 135,000 congregants across Ghana.
He spoke at the Church's 2018 synod, a meeting of its governing body. It followed the theme of "effective discipleship - the cross and our commitment".
Homosexuality remains illegal in Ghana and most African countries.
Since November 2016, South Africa has been the first and only country in Africa where same-sex couples can marry.
Ghana is a markedly more religious than many Western European nations, with more than half of adults identifying as Christian and less than five per cent defining themselves as non-religious, according to Encyclopedia Britannica.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.