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The latest count added 23 superdelegates to Clinton's count, bringing her to the magic number of 2,383.
If the count holds and Clinton wins the nomination, she would be the first woman to become the nominee of a major political party.
Her rival, Bernie Sanders, immediately pounced on the news.
"It is unfortunate that the media, in a rush to judgment, are ignoring the Democratic National Committee’s clear statement that it is wrong to count the votes of superdelegates before they actually vote at the convention this summer," the Sanders camp said in a statement.
"Secretary Clinton does not have and will not have the requisite number of pledged delegates to secure the nomination. She will be dependent on superdelegates who do not vote until July 25 and who can change their minds between now and then."
According to ABC News' latest estimates, Clinton has 1,812 pledged delegates and 571 superdelegates. Sanders has 1,522 pledged delegates and 48 superdelegates, the estimate says.
Clinton's camp called the news an "important milestone" in a statement, but urged caution.
"There are six states that are voting Tuesday, with millions of people heading to the polls, and Hillary Clinton is working to earn every vote. We look forward to Tuesday night, when Hillary Clinton will clinch not only a win in the popular vote, but also the majority of pledged delegates," campaign manager Robby Mook said in a statement.
Sanders has repeatedly blasted the nomination process on the Democratic side, which includes hundreds of unpledged superdelegates, as unfair.
"When we talk about a rigged system, it’s also important to understand how the Democratic Convention works,” Sanders said at a rally in Evansville, Indiana last month. “We have won, at this point, 45 percent of pledged delegates, but we have only earned 7 percent of superdelegates.
“So, in other words, the way the system works, is you have establishment candidates who win virtually all of the superdelegates. It makes it hard for insurgent candidacies like ours to win.”
At a campaign event in Long Beach, Calif. Monday evening, Clinton said "we are on the brink of a historic, historic, unprecedented moment, but we still have work to do."
Hundreds of delegates are at stake in the contests tomorrow night in six states -- California, Montana, New Jersey, New Mexico, North Dakota and South Dakota.
Additional reporting by Liz Kreutz.
This is a developing story. Please check back in for updates.