Washington (CNN) Donald Trump and Hillary Clinton scored huge victories Tuesday that bring them closer to a monumental duel for the White House in the fall.

Trump's political strength was on display with a clean sweep of races in Maryland, Delaware, Pennsylvania, Connecticut and Rhode Island. Clinton delivered big wins in Maryland and Pennsylvania -- the biggest prizes of the night -- along with Delaware and Connecticut. Bernie Sanders picked up his sole victory of the night in Rhode Island.

The wins for Trump -- following a massive victory last week in New York -- move him significantly closer to the 1,237 delegates he needs to win the nomination outright and avoid a contested Republican convention. That historic prospect is now the only way rivals Texas Sen. Ted Cruz and Ohio Gov. John Kasich could stop Trump from becoming the GOP nominee.

"This to me was our biggest night," Trump said in his victory speech. "I consider myself the presumptive nominee."

Clinton's big wins, meanwhile, help bolster her campaign's argument that it is time for Sanders to make a decision to stop personal and political attacks on the former secretary of state that could weaken her ahead of a showdown in November with Republicans.

She climbed on stage to cheers in her election night headquarters in Philadelphia, the city that will host the Democratic National Convention this summer.

"With your help, we are going to come back to Philadelphia for the Democratic National Convention with the most votes and the most pledged delegates," Clinton declared. "And we will unify our party to win this election and build an America where we can all rise together, an America where we lift each other up instead of tearing each other down."

General election clash

Clinton foreshadowed the potential general election clash with Trump that could center on women voters.

"The other day, Mr. Trump accused me, of playing the, quote, woman card," she said. "Well, if fighting for women's health care and paid family leave and equal pay is playing the woman card, then deal me in."

Trump struck back during his victory speech.

"I think the only card she has is the women's card," Trump said. "She has got nothing else going. Frankly, if Hillary Clinton were a man, I don't think she would get 5% of the vote."

He added: "And the beautiful thing is women don't like her, ok?"

As of 2 a.m. ET, Trump picked up at least 142 delegates on Tuesday, bringing him to 988 compared to Cruz at 568 and Kasich at 152, according to CNN estimates. Clinton won at least 214 delegates, boosting her total to 2,168, which includes 1,666 pledged and 502 superdelegates. Sanders holds 1,401 delegates, including 1,359 pledged delegates and 42 superdelegates.

There were the first signs that Sanders may be about to embrace a change of tactics, despite vowing to take his campaign all the way to the Democratic convention in July.

In a statement issued after the results rolled in, Sanders insisted that he was in the race until "the last vote is cast." But he added: "That is why this campaign is going to the Democratic National Convention in Philadelphia with as many delegates as possible to fight for a progressive party platform."

While Sanders mentioned his desire to fight to influence the issues the party will fight on in November, he did not promise to push for a personal victory in the campaign — a significant difference.

Not backing down

Trump's challengers may have one last chance to stop him from winning the nomination outright by beating him in the Indiana primary next week.

Cruz, speaking before polls closed -- in a clear sign that he expected a bad night -- slammed the media for what he said was a premature judgment that the general-election nominees would be Clinton and Trump. He branded them "New York liberals."

But he predicted things would change next week.

"I've got good news for you tonight, this campaign moves back to more favorable terrain," Cruz told a crowd in Indiana.

But Trump already has his sights on a general election — and will move further into a national campaign mode with a major foreign policy address in Washington on Wednesday, part of a process of putting a more conventional and professional foundation under his campaign — even as he insists that his wild rallies and volatile rhetoric which powered his political rise will continue.

Clinton banking on a big night

In the Democratic race, Clinton's victories build on her resounding success in New York, which stunted Sanders' momentum and left the senator -- for all his fundraising muscle and large rallies -- fending off calls from Clinton supporters to fold his campaign so that she can start exclusively targeting Republicans.

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Sanders and Clinton were competing for 384 pledged delegates on Tuesday. Clinton went into the night leading Sanders by 253 pledged delegates, according to a CNN estimate, and dominated the count among superdelegates -- party officials and activists who also have a convention vote.

At her victory speech, Clinton extended an olive branch to Sanders in an apparent effort to begin the process of unifying the Democratic Party behind her candidacy.

"I applaud Sen. Sanders and his millions of supporters for challenging us to get unaccountable money out of politics and putting greater emphasis to closing the gap of inequality," she said. "I know together we will get that done."