London - Prince William would stand by his children if they came out as gay, he said.
He spoke out on a visit to a charity that helps homeless young people who are lesbian, gay, bisexual or transgender.
It is thought to be the first time that a member of the Royal Family has visited such an organisation.
One young gay man, who asked not to be identified, asked the prince: "If your child one day in the future said 'Oh I’m gay, oh I’m lesbian' whatever, how would you react?"
William replied: "Do you know what, I’ve been giving that some thought recently because a couple of other parents said that to me as well.
"I think you really don’t start thinking about that until you are a parent, and I think – obviously absolutely fine by me.
"The one thing I’d be worried about is how they – particularly the roles my children fill – is how that is going to be interpreted and seen."
He revealed that he and wife Kate had discussed the issue to ensure they were prepared. He said he feared his children George, five, Charlotte, four, and Louis, one, could be "persecuted" because they are royal.
He said: "Communication is so important with everything, in order to help understand it you’ve got to talk a lot about stuff and make sure how to support each other and how to go through the process.
"It worries me, not because of them being gay, it worries me as to how everyone else will react and perceive it and then the pressure is then on them." William was speaking on a visit to the Albert Kennedy Trust in Hoxton, east London.