Tim Farron - an outspoken Christian - told Premier's Inspirational Breakfast programme on Wednesday he was "foolish" to say gay sex was not a sin, during last year's General Election campaign.
Responding on Twitter, Sir Vince said: "I strongly disagree with Tim Farron's personal views expressed today..."
"[The Liberal Democrats] have a long & proud record of fighting for LGBT+ rights: campaigning to repeal section 28, equalising age of consent and legislating for equal marriage.
"I will continue to champion rights and dignity.
Sir Vince's comments drew endorsements from other high-profile Lib Dem figures, including the party's president and Christian, Baroness Sal Brinton.
I strongly endorse Vince's comments below. https://t.co/Bxo1nNzNRD
— SalBrinton (@SalBrinton) January 10, 2018
During yesterday's interview, Tim Farron told Premier of his "regret" at bowing to the pressure he felt under to say homosexual activity is not sinful.
.@timfarron is entitled to his views and I know he has been troubled about the issue but I don't agree with his interpretation. I personally and politically support #LGBTQ rights - and always will.
— Willie Rennie (@willie_rennie) January 10, 2018
The Christian politician also voiced frustration that his views on sexuality drew attention away from the Lib Dem's General Election campaigning last year.
He told presenters John Pantry and Rosie Wright: "The bottom line is, of course, I did [feel pressured] and there are things - including that - that I said that I regret.
"All they wanted to do is talk about my Christian beliefs and what they actually meant.
"Foolishly and wrongly, [I] attempted to push it away by giving an answer that, frankly, was not right."
Tim Farron resigned as leader of the Liberal Democrats in June 2017, saying he felt "torn" between his faith and job; he also admitted failings in his handling of the interest in him.