St. John Paul II and children as a gift

I’m working on a presentation and want to use this alleged quotation from St. John Paul II:

And what is the best gift you can give your children? I say to you: Give them brothers and sisters.

It also comes in a variant form:

The greatest gift you can give your child is another sibling.

But did he actually say either one?

One place that gave the quotation claimed that it’s from his visit to Washington D.C. in 1979, so I scurried over to the Holy See’s website and looked at everything they had there from that visit. The closest thing was from his homily for the Mass on the Mall:

Decisions about the number of children and the sacrifices to be made for them must not be taken only with a view to adding to comfort and preserving a peaceful existence. Reflecting upon this matter before God, with the graces drawn from the Sacrament, and guided by the teaching of the Church, parents will remind themselves that it is certainly less serious to deny their children certain comforts or material advantages than to deprive them of the presence of brothers and sisters, who could help them to grow in humanity and to realize the beauty of life at all its ages and in all its variety.

I know of several other places where he talked about children as a gift (e.g., his Letter to Families), but none of them are phrased in the way the first two quotations are.

I did Google searches of the Vatican website for both of the first two alleged sayings and found nothing. (Well, thanks to Google’s penchant for searching for related words, I found lots of things, but none of them was one of the quotations in question.) Google Books was not helpful. I even tried Bing (the web search, not the singer).

My last hope is that what he actually said in DC varied from the prepared version on the Vatican website, but I can’t find a recording of that homily on YouTube.

I really don’t want this to be a fauxtation, but I’m afraid it is.