LOS ANGELES -- Hillary Clinton sailed to victory in Tuesday's primaries in New Jersey, New Mexico and South Dakota, but the night would not be a sweep for the former secretary of state, with fellow candidate Bernie Sanders pushing forward with a win in North Dakota.

But at a victory rally in Brooklyn, N.Y., Clinton laid claim to the Democratic Party's presidential nomination and with it, a piece of history, telling supporters that they were witnessing a historic moment.

"Thanks to you, we've reached a milestone. First time in our nation's history that a woman will be a major party's nominee," she said, adding that the victory "belongs to generations of women and men who struggled and sacrificed and made this moment possible."

Donald Trump, meanwhile, easily won Republican primaries in California, Montana, New Jersey, New Mexico and South Dakota, capping a day in which party leaders recoiled at the businessman's recent comments about a Hispanic judge.

Trump was conciliatory at his victory rally at one of his golf courses in suburban New York City, saying he understands what he faces in leading the Republican Party.

"I understand the responsibility of carrying the mantle, and I will never ever let you down," Trump said.

Trump, after the last of his fellow candidates dropped out last month, ended the night with enough bound delegates -- who are required by party rules to vote for him at the convention -- to secure the nomination.

In all, six states -- California, Montana, New Jersey, New Mexico, North Dakota and South Dakota -- played host to the final round of state-level Democratic and Republican presidential contests Tuesday night, with the largest prize for either party coming from California. (North Dakota's Republicans caucused in March.)

As she took the stage to raucous cheers, Clinton paused, flinging her arms wide and beaming broadly. "This campaign is about making sure there are no ceilings, no limits on any of us," she said.

"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."

Taking on Trump, Clinton accused the businessman of wanting to win "by stoking fear and rubbing salt in wounds -- and reminding us daily just how great he is."

She took to social media earlier in the evening to celebrate as well.

"To every little girl who dreams big: Yes, you can be anything you want--even president. Tonight is for you," Clinton wrote on Twitter shortly after she won New Jersey. She also took to twitter to promote a free magnet that bears her image and reads, "June 7, 2016: History made."

Another Tweet touted, "Tonight, we can say with pride that, in America, there is no barrier too great and no ceiling too high to break."

Counting support from superdelegates -- the party leaders and elected officials who can back a candidate of their choosing -- she has enough support to win the nomination at the Democratic convention in July. She would become the first female presidential nominee for either of the two major parties.

"According to the news, we are on the brink of an historic, historic, unprecedented moment," Clinton said Monday at a rally in Long Beach, Calif. " But we still have work to do, don't we? ... We're going to fight hard for every single vote, especially right here in California."

Pelosi endorsement

Clinton and Sanders were both pressing for victory in California and Montana. However, official results in California might not be known Tuesday night: more than half of Californians vote by mail, and the deadline for returned ballots isn't until Friday, as long as they were postmarked by the primary, Tuesday.

The two were locked in a close race in Montana as of late Tuesday night.

But Clinton wasted no time moving toward the general election. Her campaign announced that she would make stops next week in Ohio and Pennsylvania.

The former secretary of state, first lady and U.S. senator secured support Tuesday from House Minority Leader Nancy Pelosi, who represents a California district. And Clinton will soon have help on the campaign trail from President Barack Obama. Her 2008 opponent is to endorse her as early as this week, according to a person close to the president. The timing and venue for the endorsement hasn't been set, but Obama is appearing at Democratic fundraisers in New York today.

"At this point, there is at least one superdelegate, the one who works in the Oval Office, who is not prepared to make a public declaration of his endorsement," White House spokesman Josh Earnest said. "We'll keep you posted."

Obama called Clinton late Tuesday to congratulate her on securing the backing of enough delegates to win the nomination. Obama also called Sanders to thank him for his campaign, and the two will meet on Thursday.

Clinton and Sanders are expected to connect in the coming days, Clinton's spokesman said late Tuesday. The candidates' campaign managers spoke earlier in the day, signaling that conversations were underway about the road ahead.

But Sanders indicated he's still prepared to contest the race through the July nominating convention in the hopes of winning over superdelegates who have aligned with Clinton.

"Defying history is what this campaign has been all about," Sanders said on NBC. "I'm going to be meeting with my supporters to figure out the best way forward so we have a government that represents all of us and not just the 1 percent."

One Sanders supporter suggested the party would begin to come together sooner, however.

"We have to be unified to take on Trump, and that unity is going to begin today as soon as the polls close," U.S. Sen. Jeff Merkley, D-Ore., said Tuesday on CNN.

Dianne Feinstein of California said Sanders and Clinton should "march on to a general election together," and any Sanders plan to keep fighting until the Democratic National Convention "is going to make that much more difficult."

Sen. Claire McCaskill, D-Mo., said that for Sanders, "I think the math is unforgiving."

With Sanders' campaign still pushing forward despite Clinton's lead, Trump made a direct appeal to the Vermont senator's supporters and other Democrats.

"We welcome you with open arms," he said. "This election isn't about Republican or Democrat, it's about who runs this country: the special interests or the people."

At his victory rally in New York, Trump focused his attacks on Clinton, saying the former secretary of state "turned the State Department into her own private hedge fund."

Trump said Clinton and her husband, former President Bill Clinton, "had turned the politics of personal enrichment into an art form for themselves." He accused them of "selling access" and government contracts in order to enrich themselves and suggested Clinton used a private email server to hide it.

The businessman also previewed his coming campaign tactics, adding that he would be giving a major speech about the Clintons "probably Monday."

Looking ahead

With all 50 states' presidential primaries and caucuses in the books -- Democrats in Washington, D.C., have the nation's final contest next week -- voters in those final six states already were looking ahead to the general election.

Democratic and Republican voters alike said they have long been weighing and comparing candidates with an eye toward who could come out on top in November.

In San Diego, 82-year-old Harry Backer voted for Clinton. The retired teacher, who also worked in construction, said America needs a level-headed, grounded woman with world experience.

"I'm left of Bernie Sanders, but I know that she's the candidate that can possibly get something done," Backer said.

Izabela Biel voted for Trump in Closter, N.J. Biel said Trump's success as a businessman symbolizes the American dream for her. Biel came to the U.S. from Poland about 25 years ago, and she offered that even though he isn't the perfect candidate, she prefers him to the Democratic candidates who "want to make everybody equal."

"I grew up in communism," said Biel, 46. "I've lived it, and I absolutely know that it's proven that it doesn't work. You can't make everybody equal. That just doesn't exist in the real world."

In Albuquerque, N.M., 72-year-old retiree Thomas Ocken cast a ballot for Sanders. Ocken said he didn't think it mattered after news of Clinton's delegate count but that he wanted to cast a ballot anyway.

"I think Democratic Socialism is much more fair. I'm not afraid of socialism," Ocken said. "I don't think he'll win. At least he'll put more pressure on Hillary."

Jonell McLain, 70, of Ventura, Calif., another Sanders supporter, predicted a "divisive and incredibly painful" election this year while praising Sanders for pushing Clinton to adopt more liberal stances.

"This campaign is rallying people and showing that we're ready for something more extreme," McLain said. "I've never heard that -- and I was around in the '60s."

Information for this article was contributed by Julie Pace, Ken Thomas, Catherine Lucey, Hope Yen, Stephen Ohlemacher, Lisa Lerer, Mary Clare Jalonick and Erica Werner of The Associated Press and by Margaret Talev, Jennifer Epstein, Arit John, Terrence Dopp, Angela Greiling Keane and Mike Dorning of Bloomberg News.

A Section on 06/08/2016