Following the 5-4 Supreme Court decision, which was widely lauded across the Western world, the 91-year-old leader, known for his fiercely anti-homosexuality stance, said he would "get down on my knee and ask [Obama's] hand" before condemning marriage equality.
Mugabe made the comments during his weekly radio interview with the country's national radio station, ZBC, on Saturday.
"I've just concluded since President Obama endorses the same-sex marriage, advocates homosexual people and enjoys an attractive countenance thus if it becomes necessary , I shall travel to Washington DC, get down on my knee, and ask his hand," he said.
"I can't understand how this people dare to defy Christ's explicit orders as our Lord prohibited mankind from sodomy," he added.
He also claimed that Washington was being controlled by "perverted Satan-worshippers who insult the great American nation", according to Nigerian new website Naij.com.
At a 2013 campaign rally, Mugabe had condemned Obama for forcing homosexuality on the continent. "We have this American president, Obama, born of an African father, who is saying we will not give you aid if you don't embrace homosexuality. We ask, was he born out of homosexuality?"
Homosexuality is illegal in Zimbabwe and, in previous speeches, Mugabe has told gay people to go to "hell" and stated that those of homosexual orientation are lower than "pigs, goats and birds".
"Let Europe keep their homosexual nonsense there and live with it. We will never have it here. The act [of homosexuality] is not humane," he said in a July 2013 speech to his Zanu PF party supporters. "Any diplomat who talks about homosexuality will be kicked out. There is no excuse and we won't listen to them."
Elsewhere on the African continent, Zimbabwe's neighbour, Mozambique, yesterday scrapped a colonial law dating back to 1886 which criminalised homosexuality, bringing in a new penal law which also decriminalized abortion.
The original law had targeted anyone "who habitually engages in vices against nature" and was punishable by up to three years of hard labor. Gay rights activists called the decision as a "symbolic victory" for gay rights in Africa.
The US decision to legalize gay marriage came just before LGBT Pride marches took place around the world, with American landmarks such as the White House being lit in rainbow colors to mark the historic ruling. However, in Turkey, those celebrating a gay pride march were stopped in their tracks by Turkish police who used water cannon, tear gas and rubber pellets to disperse crowds.
crawled from Newsweek.com