Lynne Featherstone, the international development minister, said she would sign a petition to ban Page 3 because it had a "deleterious effect" on women.
Mrs Featherstone said she had experienced verbal abuse for her views on women's rights when she was equalities minister until this month. Mr Cameron has appointed her as "ministerial champion" to tackle violence against women across the world.
The petition, set up by Lucy Holmes and entitled "Take the bare boobs out of The Sun", had more than 30,000 signatures last night.
Admitting she would be called "mean" and "sour-faced" by some people, Mrs Featherstone said: "There is a real argument about what is OK in the public space. If you are on the Tube you may find Page 3 is facing you and your young daughter and you may not want that to be a role model for her.
"There is an army on the other side hurtling abuse. It's not simply about equal pay. It's about the constant drip, drip of women being sexualised in the public space [which] has a great bearing on attitudes and domestic violence.
"When you know that one in four women experience domestic violence in their life, two women are killed each week by their partner or husband, there is a very long way to go. While a lot of blokes say 'You are mean, sour-faced, whatever – it's harmless', actually it's not harmless at all."
OP: Page Three has always been more Carry On than anything sinister. If you don't like it, here's the thing...don't buy the paper. I don't like The Sun. But I don't think its the job of government to whip up things like this.
Besides, the two biggest tits I've seen are always on the front page, not on page three. Cameron and Clegg.