Today's meeting took place while Blair, a practicing Catholic and human rights lawyer, is in Rome to participate in the plenary assembly of the Pontifical Academy of Sciences on the theme: "Vanishing Youth? Solidarity with Young People in an Age of Turbulence."
Blair, a barrister who is a Queen's Counsel, was listed by the Vatican as an outside expert.
In a press statement, the United Kingdom's ambassador to the Holy See, Francis Campbell, said that the meeting between the two was a surprise for Blair, and that she was "thrilled" by the unexpected conversation, which took place in the Pope's library.
Blair, mother of four, commented to ZENIT about the assembly of the Pontifical Academy of Sciences: "I said today that what I think is really important is that we should listen to our young people and have faith in them, and that through the family and through making space and time for our children then together we can learn from each other as to how we can meet these challenges."
"It's a great thing that there are some youth here to listen and who will give us their feedback at the end ... In the true spirit of learning and sharing together," she said.
When asked how the Church can translate what is being discussed here at the Vatican into national strategies for helping children worldwide, she said: "The Church has a very important role to play in this of course, because the Church is one of the very few organizations which actually is everywhere in the world."
"So, the dialogue we have here has resonance across the world, but it has to be a dialogue of belief, of ideas and values, which can then be used in a pile of particular social and political contexts across the world," she added.
"There is not an absolute, 100% answer for everywhere," continued Blair, "but what I do think is interesting is that we can learn from each other. I spoke of some more practical examples but fundamentally it's values, the promotion of an inherent and common human dignity and concentrating on seeing God in the other that matters."
Blair added: "It's a message we can't stress enough!"