Senior MP Nigel Evans said he was "clearly a second class Christian, but a first class gay" given he could not get married in a church in England.
Former Army officer Bob Stewart, meanwhile, said he was wrong to have voted against equal marriage legislation "because I've seen the joy it's given so many people".
Mr Evans said: "I mentioned the royal wedding. A billion people will be tuning in to watch that happy event. I'll certainly watch it.
"But whilst I am watching that happy event, one thing will flash through my mind, and that is that I am a Christian.
"Clearly a second class Christian, but a first class gay. Why? Because I wouldn't be allowed to walk down the aisle with somebody that I loved and get married in a church in England.
"My message to Justin Welby is I understand why, because of the church in Africa and some other countries where they're not as progressive as we are.
"But he needs to show leadership. He really does, in our country, to ensure that gay Christian people can get married and enjoy a big day, just as Harry and Meghan are going to do on Saturday."
Mr Stewart then intervened, saying: "I voted against the Equal Marriage Act, and I was wrong. I was wrong, because I've seen the joy it's given so many people.
"I was wrong. But I do think the church, the established church of our country, should follow what this House has decided and that actually gay people should be allowed to marry in church."
His comments prompted shouts of "hear, hear" from other MPs, while Mr Evans said: "Breaking news. Absolutely superb.
"(Mr Stewart) has just spoken about how his views were in the past, and what his views are today.
"I have to say if (Mr Stewart) can make that progression, I do rather hope that the Archbishop of Canterbury is listening and he too can make that sort of progression, in order that Christians in this country are able to enjoy a big day just as Harry and Meghan will do on Saturday."
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