"I support that very strongly and we'll campaign for that when it comes," he said.
Up until now, Mr Kenny has avoided making any comment on his view of gay marriage.
Tánaiste Eamon Gilmore said the right of gay people to marry was an "important issue".
But the Catholic Church indicated it will oppose the gay marriage referendum, saying any change to the nature of marriage would "undermine" it as the fundamental building block of society.
Bishop Denis Nulty said the Catholic Church will continue to hold that the differences between a man and woman are "not accidental to marriage but fundamental to it".
He says that children have a "natural right to a mother and a father" and that this is the best environment for them where possible.
"The Church will therefore participate fully in the democratic debate leading up to the referendum and will seek with others to reaffirm the rational basis for holding that marriage should be reserved for the unique and complimentary relationship between a woman and a man from which the generation and upbringing of children is uniquely possible," he said.
The Government agreed to hold a referendum on civil marriage for same-sex couples in the first half of 2015.
Earlier this year, a think-tank in charge of examining the Constitution voted overwhelmingly to recommend a change to allow for civil marriage for same-sex couples.
Gay and Lesbian Equality Network chairman Kieran Rose said the groups were "delighted" with the decision to hold a referendum on equal access to civil marriage for lesbian and gay people in 2015.
TD John Lyons' VIEW: SEE PAGE 15