WASHINGTON — Donald Trump swept all five Northeastern primaries Tuesday, cementing his position as the most likely Republican presidential nominee and giving him a big surge of delegates and energy heading into what could be a final showdown next week with Ted Cruz in Indiana.

Trump won by comfortable margins in each of the five East Coast states — Rhode Island, Connecticut, Pennsylvania, Delaware, and Maryland — and is now in a commanding role with just 10 states left to vote.

“I consider myself the presumptive nominee, absolutely,’’ Trump said from Trump Tower in Manhattan. “When the boxer knocks out the other boxer, you don’t have to wait around for a decision. That’s what’s happening.’’

Trump has won 12 out of the last 15 primary contests, capped by his recent six-state run that started last week with New York. His sweep Tuesday was so dominant that all the races were called within 40 minutes after polls had closed. His margins were on track to be higher than they have been in previous contests, with about 60 percent of the vote in early results.

Trump — who earlier in the evening attended a gala in New York sponsored by Time magazine that honored the world’s most influential people (Trump made the list) — essentially declared himself as the winner of the race.

“As far as I’m concerned, it’s over,’’ he said, calling for the Republican Party to unify around him. “Senator Cruz and Governor Kasich should really get out of the race. They have no pathway.’’

Trump also launched a ­gender-tinged attack on Democratic front-runner Hillary Clinton, offering a taste of the potential general election matchup.

“Frankly, if Hillary Clinton were a man, I don’t think she’d get 5 percent of the vote,’’ he said as New Jersey Governor Chris Christie’s wife, Mary Pat, rolled her eyes behind him. “The only thing she’s got going is the woman’s card. And the beautiful thing is, women don’t like her.’’

Clinton had answered that charge Tuesday in her victory speech.

“If fighting for women’s health care and paid family leave and equal play is playing the woman card, then deal me in!’’ she said to loud cheers in Philadelphia.

Cruz, the last and biggest roadblock to Trump’s quest for the nomination, faces two hurdles: math and momentum. The Texas senator now has no mathematical chance at winning the nomination outright. His only hope is to deny Trump enough delegates to clinch the nomination and force a contested convention in Cleveland in July. But Trump has the advantage of momentum, particularly after a pact between Cruz and Governor John Kasich of Ohio to try to divvy up several of the remaining states seemed to crumble this week.

Indiana, which votes next Tuesday, is shaping up to be the last stand for Cruz and the anti-Trump forces.

“Tonight, Donald Trump is expected to have a good night,’’ Cruz said Tuesday night from Knightstown, Ind., about 10 minutes before polls closed. “Tonight this campaign moves back to more favorable terrain.’’

Cruz spoke from the same gym where the movie “Hoosiers’’ was filmed. It is about a scrappy small-town basketball team that uses a slow, defensive style to overcome long odds and win the state championship with a last-second shot.

Cruz has been grinding it out on the tedious work of wooing uncommitted delegates around the country and trying to stack rosters of committed delegates with his supporters, who would presumably be sprung in his favor if Trump fails on a first convention ballot.

But Cruz also desperately needs a win to stem Trump’s growing advantage. And even while he has tried to emerge as the chief alternative, he came in third place in four out of five states on Tuesday — trailing Kasich.

Cruz has spent most of the past few days in Indiana, appealing to evangelicals in the same sort of effort that helped him win Iowa and Wisconsin.

Cruz wants to win over Kasich supporters in Indiana, who tend to be more moderate. Although Kasich said he won’t compete in Indiana under his agreement with Cruz to try joint tactics to block Trump, the Ohio governor still urged his supporters to vote for him — which seemed to undermine the spirit of the deal.

And Trump right now is leading in several polls of Hoosier voters. A Fox News poll released Sunday had Trump over Cruz and Kasich by eight percentage points. Even without Kasich in the lineup, Trump still had a narrow lead over Cruz.

On Wednesday night, Trump is expected to travel to Indianapolis to receive the endorsement of legendary former Indiana University basketball coach Bobby Knight. Like Trump, Knight has a reputation for brash plainspokeness peppered with occasional vulgarities.

Indiana has 57 delegates up for grabs, the largest haul still available aside from California. If Trump loses the state, it will be significantly harder for him to gather the 1,237 delegates needed to win the nomination outright and avoid a contested convention.

Still, Trump’s victories Tuesday night arrived as Republican establishment figures are beginning to concede that Trump is the most likely nominee. Trump, meanwhile, seems as unpredictable as ever.

During his victory speech last week, after a blowout win in New York, he seemed subdued, even referring to his rival as “Senator Cruz.’’ The next day, it was back to “Lyin’ Ted.’’ By Monday, he was ridiculing the way Kasich eats while on the stump.

Warring factions have emerged inside the Trump campaign. One side, represented by his campaign manager Corey Lewandowski, repeats the mantra “Let Trump be Trump.’’ Another faction, represented by newly hired strategist Paul Manafort, wants Trump to appear more presidential and woo party leaders, give policy speeches, and even begin using a teleprompter.

Trump is scheduled Wednesday to deliver a foreign policy speech at the Mayflower Hotel in Washington, D.C. During his victory speech, he said he would avoid taking any firm positions and would not outline a Trump Doctrine.

“You have to have flexibility,’’ he said. “I can’t say: ‘This is my doctrine, I will not move,’ because the world changes. Countries change. Leaders change.’’

Answering to charges that he is playing a role and would shift for the general election, he said, “Why would I change? If you have a football team, and you’re winning, and then you get to the Super Bowl, you don’t change the quarterback, right?’’

“I’m not changing,’’ he added. “I may act differently but my thought process is the same.’’

The turmoil in the Republican primary was illustrated in some of the exit polls of voters in Connecticut, Pennsylvania, and Maryland on Tuesday.

In Pennsylvania, for example, nearly 60 percent said the Republican primary had divided the party, while 39 percent said it had energized it. Some 61 percent of Republican voters there said that they felt betrayed by Republican politicians. And in one indication that many voters believe Trump’s repeated claims that the primary process is “rigged,’’ 46 percent said Cruz ran the “most unfair campaign,’’ compared with 33 percent who said the same of Trump.

Heading into Tuesday night, Trump had 845 delegates, while Cruz trailed with 559 and Kasich with 148. In order to win 1,237 bound delegates needed to clinch the nomination on the first ballot, Trump would need to win at least 63 percent of the remaining delegates.

On Tuesday night, he was poised to win by big enough margins to lower that bar.

He won all 16 delegates in Delaware and was on the cusp of winning all 38 delegates in Maryland and all 28 delegates in Connecticut. He was likely to win a significant share of Rhode Island’s 19 delegates, which are awarded proportionally.

Trump won Pennsylvania easily, but the state’s quirky delegate system could still benefit other candidates. Only 17 delegates go to the statewide winner; the other 54 delegates were elected on the ballot, and are free to vote for whomever they wish at the convention. Each campaign was working to get a slate of their supporters elected as delegates.

Matt Viser can be reached at matt.viser@globe.com.