Hillary Clinton: Becoming Presumptive Democratic Nominee Will 'Send a Signal Around the World'

— -- On a historic night, Hillary Clinton called her new status as the presumptive Democratic presidential nominee — the first woman of any major party to claim that mantle — “a real milestone.”

“It is, of course, symbolic, but symbols mean something, and symbols can often can spark hope and action in people, particularly young people,” Clinton told ABC News’ David Muir in an exclusive interview. “I think it will be a real milestone with my nomination for our country, but it will also send a signal around the world.”

Muir spoke with Clinton at the Brooklyn Navy Yard just moments before she took the stage to celebrate her victories in Tuesday’s primaries. Clinton reached the delegate threshold needed to clinch the Democratic nomination on Monday night with new commitments from superdelegates. Six states held nominating contests on Tuesday: California, New Jersey, Montana, South Dakota and New Mexico and North Dakota.

The pivotal moment in her quest for the White House comes eight years, to the day, after she delivered a very different kind of speech to a crowd of supporters in Washington, D.C. — a concession to then-Sen. Barack Obama.

Back then, she vowed to do her part to bring the Democratic Party together, and tonight she said she would focus her attention to unifying the party once again and mending divisions after a contentious primary season with her rival, Sen. Bernie Sanders.

“Our campaigns are talking to one another,” Clinton told Muir of her discussions with Sanders’ team. “I want to unify the party. I look forward to talking with him personally, because I think his campaign has been a really dynamic and exciting experience for the millions of Americans — particularly young people — who supported him.”

She added that she wants supporters of the Vermont senator “to know that I’m going to be working on a lot of the same issues that Sen. Sanders and I spoke about, that we both care about, and that we have so much more in common than we do with the Republican presumptive nominee, Donald Trump.”

Clinton said she was not concerned that Sanders supporters might instead turn to her presumed Republican rival in the general election.

“Anyone who supported Bernie Sanders, who thinks we should raise the minimum wage, who thinks that we should have universal health care coverage, who thinks that the wealthy have not paid their fair share,” she said, “would certainly not find that Donald Trump’s views are in line with theirs.”

Still, even as she relished the historic moment for herself and for the nation, Clinton acknowledged the long road ahead.

“It’s going to take some real time to absorb and reflect on what it means to me personally, what it means to our country,” she said. “But just as I look at this night and feel the joy and the sense of both possibility and responsibility, it means a great deal to have the faith and trust of so many people who share the view and vision I have for our country, and I’m going to do everything I can not to let them down.”

For more of Muir’s exclusive interview with Clinton, tune in to “Nightline” tonight and “Good Morning America” and “World News Tonight With David Muir” on Wednesday.