Northern Ireland's regional health minister resigned on Monday after saying that children of same-sex couples were more at risk of being abused or neglected.
Jim Wells was also placed under investigation by police over alleged comments made to a lesbian woman while out campaigning for next week's general election.
Wells said in a statement that he and his family had been attacked on social media "in a deeply personal, nasty and, in some cases, threatening way".
The issue of same-sex marriage is hugely controversial in Northern Ireland -- the only part of the United Kingdom that does not allow it and which also bans abortion.
Northern Ireland's regional assembly was debating same-sex marriage on Monday but attempts to legalize it have been rejected by local politicians in the past.
The neighboring Republic of Ireland is set to vote to allow same-sex marriage in a referendum next month.
Wells, a devout Christian from the Democratic Unionist Party, apologized last week after saying at a campaign event that "facts show you certainly don't bring a child up in a homosexual relationship".
He is also being investigated following a complaint by the daughter of a lesbian woman who said that her mother had been upset following an exchange with Wells when he came campaigning to their house.