Transcript of Clinton's MLK Interview on NBC's "Nightly News"

WILLIAMS: Senator, first of all, this is-- this is almost a national talisman. Talk about the emotional impact this place.

CLINTON: Well, it has an incredible impact on me. Because I remember where I was and what I was doing when I heard that Dr. King had been killed. I had met him as a young woman, when I was 14. And it really opened my life even as we look out at where we are in our country today, with all the unfinished business of poverty and economic challenges and a war that we need to end, it is so reminiscent of what he was talking about when he died. And we have to honor that.

WILLIAMS: You see the glass as half empty or half full? As they said during the Constitutional Convention, is the sun rising or setting where race, as a topic in this country, is concerned?

CLINTON: I believe the sun is rising. I believe the glass is half full. But whether you fill it to the top, or the sun actually makes it into the sky without being obscured by clouds and storms, is really up to us. It is not only up to those of us in public life, it is up to each of us in our personal lives.

WILLIAMS: How can you become the leading voice for-- matters of race for fulfilling Dr. King's dream with an African-American also in the race? Or does it matter whose voice is the leading voice as long as there's progress on the subject?

CLINTON: I think there are so many leading voices. And-- I am here as a beneficiary of Dr. King. The Voting Rights Act helped me as well as helped those who were waiting in line to vote and being turned away in-- so many places across the south. I was a young person when we reformed and amended the Constitution so that you could vote at the age of 18.

So the emphasis on empowerment and participation that was at the core of the Civil Rights Movement has benefited me and every American whether we know it or not.

WILLIAMS: Final question. It's been theorized that not having a national conversation on race was perhaps one of the-- the missing elements of your husband's presidency. Can you pledge yourself to a national conversation on race?

CLINTON: Well, Brian, I believe that we have to continue it. It is an ongoing conversation. It should never end. And we not only need to talk about race, we need to talk about gender. We need to talk about religion. We need to talk about the full range of the categories in which we are often placed by ourselves and by those who look at us.

I think, for me, as a white woman, you know, Dr. King was a category breaker. You know, he was reaching across all of those divides. And, as president, that's what I want to be as well. Here at home and around the world. We've got to find ways for us to connect with each other's common humanity.