Speaking with the gay website PinkNews, Theresa May answered a questioned submitted by a reader which asked whether she wanted the Church to solemnise gay marriages.
She said: "As the established church, it is in a different legal position from other churches or faith groups, so the law equalising marriage had to recognise that.
"I strongly support equal marriage, and I know that these debates will continue, but it will have to be for the church as a whole to decide if it wants to make a change to its canon law."
Under canon law, the Church of England can exercise self-determination when it comes to the issue of whether or not it performs gay marriages.
Mr May added: "We were very clear when we introduced the equal marriage legislation that it was not about forcing the Church of England to conduct marriage ceremonies, but removing a legal injustice."
In the PinkNews interview, Theresa May also refused to commit the UK to remaining in the European Convention on Human Rights but insisted that LGBT rights would be protected "regardless of any changes to the legal framework".