(CNN)Hillary Clinton claimed her place in history Tuesday as America's first female presumptive presidential nominee but rival Bernie Sanders is refusing to drop his bid despite overwhelming odds.

The former secretary of state immediately pivoted from her victory to a full bore assault on the presumptive Republican nominee Donald Trump and made a sweeping effort to reach out to Sanders supporters in an attempt to unify Democrats.

Primary results maps

But hours after Clinton's euphoric victory rally in Brooklyn, Sanders spoke before a roaring crowd of his own in California to declare "the struggle continues." The Vermont senator pledged to stay in the race through next week's primary in Washington, D.C., and to fight on for social, economic, racial and environmental justice at the Democratic National Convention in Philadelphia.

But he did not specifically commit to pursuing his fight for the nomination at the convention, leaving his ultimate intentions unclear.

Obama's call

President Barack Obama, who waited until voting ended in the last six primary states to weigh in on the race, called both candidates to congratulate them for "running inspiring campaigns that have energized Democrats," according to a White House statement.

But the President, who will meet with Sanders Thursday at the Vermont senator's request, clearly sided with Clinton by lauding her for "securing the delegates necessary to clinch the Democratic nomination for President."

"Her historic campaign inspired millions and is an extension of her lifelong fight for middle-class families and children," the statement said.

Reaching the highest peak yet in a tumultuous and trailblazing political career, Clinton claimed victory exactly eight years after folding her 2008 Democratic primary campaign against Obama.

"Thanks to you, we've reached a milestone," she said during a speech in Brooklyn. "Tonight's victory is not about one person. It belongs to generations of women and men who struggled and sacrificed and made this moment possible."

Meet the women who came to see Clinton make history

Her long-awaited moment of celebration came as she notched wins in the night's primaries in New Jersey, South Dakota and New Mexico Democratic primaries, according to CNN projections. By 2:30 a.m. ET, she had a lead of 400,000 votes in the California primary, which has 475 delegates -- the most on offer in the entire nominating season. Sanders won victories in North Dakota and Montana.

Clinton took the stage in Brooklyn to an explosion of cheers from her crowd, in the kind of eruption of enthusiasm that has been fleeting during much of her campaign. Clearly delighted, she stood with her arms outstretched on stage, savoring the adulation.

Reaching out to Sanders supporters, Clinton praised the Vermont senator for his long public service and mirrored some of his progressive economic rhetoric. She played down any notion of divisions and said their vigorous primary campaign was "very good for the Democratic Party and for America."

But in a sign of the task she faces in uniting the party, Sanders supporters loudly booed her name when he said he had received a "gracious" call from his rival and said he had congratulated her on her victories on Tuesday.

Sanders confounded the notion that the end of the state primary races would mean the end of his campaign.

"Next Tuesday, we continue the fight in the last primary in Washington DC," Sanders said. "We are going to fight hard to win the primary in Washington, D.C., and then we take our fight for social, economic, racial and environmental justice to Philadelphia."

"I am pretty good at arithmetic and I know that the fight in front of us in a very, very steep fight."

But Sanders vowed to fight on for every delegate and every vote.

Clinton vs. Trump

While Sanders signaled that he was not yet ready to fold a campaign that started with him as a fringe candidate and ignited a startling grass roots uprising that won more than 10 million votes, Clinton looked ahead to the general election.

Clinton intensified her assault on Trump, laying out a case that his values and rhetoric are incompatible with American principles and that he's "temperamentally unfit" to be President.

"He is not just trying to build a wall between America and Mexico. He is trying to wall of Americans from each other. When he says let's make America great again, that is code for let's take American backwards."

She hit Trump hard for his recent attacks on a judge with Mexican ancestry along with mocking a disabled reporter and calling "women pigs."

"He wants to win by stoking fear and rubbing salt in wounds and reminding us daily just how great he is."

Clinton also signaled a robust challenge to Trump resonating with gender and personal themes. She spoke of how her late mother, Dorothy Rodham, taught her "never to back down from a bully."

Sanders faces an existential campaign question. He is grappling with whether to honor his vow to fight on to the Democratic National Convention next month or accept the electoral mathematics that give him no viable path to victory and join Clinton to unite a party divided by a much more competitive primary race than expected.

CNN's Brianna Keilar reported that the campaign managers for Clinton and Sanders are in touch, keeping the lines of communication open so they can eventually unify the party, according to a source familiar with the conversations.

The New York Times reported the Sanders campaign is about to undergo a significant reduction in staff. A top campaign official would neither confirm nor deny the report to CNN. But notably, as the campaign reaches the end of the primary season, the campaign has not moved to staff key battleground states and little appears in the works beyond recent promises to fight to the convention.

Trump's controversy

For Trump, the question Tuesday was how he would extricate himself from the political hole opened up by his controversial comments about a judge of Mexican descent who is overseeing a lawsuit aimed at Trump University. His accusation that the judge is biased because of his ethnicity has horrified senior GOP leaders who recently reluctantly endorsed him. He tried to neutralize the furor with a statement Tuesday saying his comments had been "misconstrued."

Amid the furor, Trump, who won the Republican contests Tuesday, delivered a more conventional speech that seemed a departure from the free wheeling approach he often takes. Using a teleprompter -- notable for someone who has blasted Clinton for being scripted -- Trump attacked Clinton and called for GOP unity. For one night at least, it seemed that the unpredictable billionaire had heeded calls by the GOP establishment -- which he built a campaign on vilifying -- to rein himself in for the good of the party.

"We are only getting started and it is going to be beautiful," he said.

He didn't mention the judge during his speech and instead sought to convey that he understood his new role as the leader of the GOP.

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

A top campaign adviser told CNN's Jim Acosta that Trump's speech was "very important to recovering from these five bad days."