"Look, I think everyone can have their own opinion. I don't agree with Margaret's opinion," the Australian No.1 said following her first-round win at the French Open in Paris.
"That's why Casey was, obviously, very adamant about that and I wanted to support my friend and that's why I sent out my first tweet in a very long time.
"And, look, it's just not something that I agree with. I think we definitely should have it (same-sex marriage) in Australia."
Stosur said she found it hard to believe Margaret Court Arena's name would ever change, but suggested some players may request not to play on it.
"The court's named Margaret Court Arena because of what she did in tennis, and that's why basically," she said.
"But I guess we'll cross that bridge when we all get down to the Australian Open next year and (see) who wants to play on Margaret Court Arena and who doesn't, and we'll go from there."
Olympian John Millman and teenage wildcard Jaimee Fourlis are also opposed to Court, who wrote in a letter to The West Australian newspaper last week: "I believe in marriage as a union between a man and a woman as stated in the Bible."
"It's a little bit inappropriate," Millman said of Court's views.
"I have a lot of time for Casey. I think she's a great person and I think she's a great mother.
"I'm all for any type of relationships. The more people get along the better and so it's a little bit disappointing.
"I just think in this day and age, there's so much worse things happening in the world.
"It's not a bad thing. I think it's a great thing when two people, regardless of their gender, find love and whatever."
Fourlis agreed with her contemporaries.
"I love Casey and two women can parent as good as a man and a woman," the 17-year-old said.
"I've seen the way Casey is parenting and her two kids are unbelievable. They're incredible."
- AAP
