"We don’t worry ourselves about the goings-on in Europe," he told thousands at the burial of deputy intelligence chief Menard Muzariri, who died on Monday.
"About the unnatural things happening there, where they turn man-to-man and woman-to-woman. We say, well, it’s their country. If they want to call their country British Gaydom, it’s up to them. That’s not our culture. We condemn that filth.
"We get alarmed when these countries have the audacity to schedule us as an item to discuss in their parliament."
Homosexuality is illegal in the southern African country. While the Gays and Lesbians of Zimbabwe (Galz) association is allowed to operate, it suffers police harassment.
"We must unite in opposing and condemning the sanctions," he said.
"We must demonstrate that we are ready to defend our country and sacrifice our lives. The enemy will try by all means to destroy us, but if we are united, we are strong."
Mugabe and members of his inner circle were slapped with EU and US sanctions in 2002 following disputed presidential elections.
His call for unity comes in the wake of widening cracks in the power-sharing deal with Prime Morgan Tsvangirai, a political rival.
Zimbabwe is drafting a new constitution to pave the way for new elections, following disputed 2008 polls that led to the unity government, but the process was often marred by violence.
Last month, Tsvangirai threatened to pull out of the unity government following the arrest of his energy minister, Elton Mangoma.