(AP) -- Claiming her place in history, Hillary Clinton declared victory Tuesday night in her bruising battle for the Democratic presidential nomination, becoming the first woman to lead a major American political party and then immediately taking aim at Republican Donald Trump.

"Tonight's victory is not about one person," Clinton said. "It belongs to generations of women and men who struggled and sacrificed and made this moment possible."

Clinton spoke at an emotional rally in Brooklyn, eight years to the day after she ended her first failed White House run. She had already secured the delegates needed for the nomination, according to an Associated Press tally, but added to her totals with victories in New Jersey and several other states.

Vermont Sen. Bernie Sanders, Clinton's only remaining rival, has insisted he still has a narrow path to the nomination. Still, Clinton made a direct appeal to his supporters, recalling the raw emotions of her own supporters when she lost to Barack Obama in the 2008 Democratic primary.

"It never feels good to put our heart into a cause or a candidate you believe in and come up short," she said. "I know that feeling well. But as we look ahead to the battle that awaits, let's remember all that unites us."

The Democratic race was ending amid new turmoil among the Republicans. GOP leaders recoiled at Trump's comments about a Hispanic judge, with one senator even pulling his endorsement.

Trump capped his difficult day with victories in New Jersey, New Mexico, South Dakota and Montana. He was muted his victory rally, saying he understands "the responsibility" of leading the Republican Party. He also made a direct appeal to dejected Sanders supporters and other Democrats.

"This election isn't about Republican or Democrat, it's about who runs this country: the special interests or the people," he said. Trump vowed to deliver a major speech next week on Clinton and her husband, former President Bill Clinton.

Clinton spent much of her own victory speech targeting Trump, previewing a tough general election campaign.

"He wants to win by stoking fear and rubbing salt in wounds - and reminding us daily just how great he is," Clinton said, her voice dripping with sarcasm.

Clinton's win in New Jersey came a day after she secured the 2,383 delegates she needed to become first female presumptive nominee of a major political party, according to an Associated Press tally. Her total includes pledged delegates won in primaries and caucuses, as well as superdelegates - the party officials and officeholders who can back a candidate of their choosing.

After her win in New Jersey, Clinton had 2,441 delegates to Sanders' 1,616. That count includes both pledged delegates and superdelegates.