David Jackson

USA TODAY

Donald Trump went five-for-five in sweeping a set of northeastern primaries Tuesday and declared himself the "presumptive" Republican nominee for president in the face of allied opposition from rivals Ted Cruz and John Kasich.

"As far as I'm concerned, it's over," Trump said in claiming easy victories in Pennsylvania, Maryland, Connecticut, Rhode Island and Delaware. He said, "this is a far bigger win than we even expected — all five."

Citing a large number of delegates and votes in the face of Republican establishment opposition, the maverick businessman said "the best way to beat the system" is to have evenings like this.

Cruz and Kasich, who have formed a loose alliance to try to block Trump in some future contests, are hoping to pick up some delegates after Tuesday's primaries, but their totals will likely be minimal in the wake of Trump's landslide wins.

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While his rivals argue that Trump would lose the fall election to Democrat Hillary Clinton, Trump said during his victory rally that he would beat the Democrat easily, and that the only thing she has going for her is "the women's card ... If Hillary Clinton were a man, I don't think she'd get 5% of the vote."

The GOP front-runner also said that Cruz and Kasich are hurting themselves with their "faulty deal," and both should exit the Republican race because they "have no path — zero path — to victory."

Cruz, headed for a third-place finish behind Kasich in many of Tuesday's contests, dismissed the results even before they were announced, reminding supporters in Indiana that the northeast is Trump's home region. The Texas senator said his campaign now "moves back to more favorable terrain," starting next week in Indiana and ending June 7 in California.

Trump also vowed to take Indiana, calling it "a great state" where he has "many, many friends."

Both Trump and Clinton, who also scored primary wins Tuesday, began turning toward each other over the prospect of a fall election battle. Clinton said Trump is dividing the nation, while Trump said "Crooked Hillary" would be a weak president.

The Republican front-runner also said the Democratic Party has treated Clinton opponent Bernie Sanders badly, and the Vermont senator should run in the fall as an independent.

Coming off a big win a week ago in his home state of New York, Trump seemed poised to move within striking distance of the 1,237 delegates he needs for a first-ballot victory at the Republican convention in July.

While Trump may collect more than 100 of the 172 delegates at stake on Tuesday, his precise total is uncertain. In Pennsylvania, 54 delegates are not bound to any particular candidate, though they can endorse one.

Trump entered Tuesday's contests with 845 delegates, according to the Associated Press, followed by Cruz at 559 and Kasich at 148.

In claiming his latest victories, Trump called for Republican unity behind his candidacy, though Cruz and Kasich have vowed to continue fighting up until the convention opens July 18 in Cleveland.

Anti-Trump political action committees also vowed to soldier on. “Even if the media yearns to declare this race over, the path to 1,237 delegates remains narrow for Trump, and he just left the most favorable part of the map for him in the northeast," said Rory Cooper, a senior adviser for the organization #NeverTrump.

Little more than a month to go before the end of primary season, there is some question as to how solid the newly formed partnership between Cruz and Kasich is.

For one thing, the agreement covers only three states. Kasich has agreed not to campaign against Cruz in next week's Indiana primary, while Cruz plans to defer to Kasich in Oregon on May 17 and New Mexico on June 7.

Kasich, however, says his supporters in Indiana are still free to vote for him, and he spent part of Tuesday in Indianapolis visiting with potential delegates and fundraisers, as well as Republican Gov. Mike Pence. Appearing on NBC's Today show, Kasich called the agreement “a matter of resources” and said he doesn't “tell voters what to do."

Trump has mocked the Cruz-Kasich alliance effort, calling it "collusion" that won't work.

Both Cruz and Kasich are trying to block Trump from winning on a first ballot at the convention, which begins July 18 in Cleveland. If that happens, many delegates would be unbound and free to vote for any candidate. Cruz and Kasich said delegates would turn to them on subsequent ballots out of concern that Trump would lose the fall election badly to Democrat Hillary Clinton and take other Republican candidates down with him.

"The bottom line is Donald Trump cannot beat Hillary Clinton," Kasich said on NBC. "If we don't beat Hillary Clinton, the Republican Party is going to give up the Supreme Court, we're going to lose the United States Senate."

Cruz, who has challenged Trump to a debate in Indiana, told a local radio station he will tell Hoosier State residents that a vote for Trump now amounts to a vote for Clinton in the fall. Cruz said Trump is running "a Kim Kardashian campaign," one that is "based on yelling and screaming and cursing and insults."

During his primary night speech, Cruz denounced the news media and claimed it favors a Trump-Clinton election in part because they are both "New York liberals," and Clinton would win the contest easily.

"Donald Trump is the one man on Earth Hillary Clinton can beat in a general election," Cruz said.

A heckler in the crowd yelled to Cruz that he is not eligible for president because of his Canadian birth. As security escorted the man out, Cruz asked backers to keep their hands off the protester and added: "If this were a Trump rally, I would be encouraging people to punch him."

Joan Connelly, a Republican from Bethesda, Md., said she voted for Kasich, despite reservations about all three candidates. She called the Ohio governor "the least" objectionable, but added: "I hope the convention's open."

Contributing: Nicholas Zazulia, Medill News Service