Republican Donald Trump and Democrat Hillary Clinton regained their stride in the presidential race Tuesday night, winning their respective primaries in New York — and sending a message to their rivals that their campaigns are back on track after recent stumbles. 

Trump, in his home state, notched what appeared to be his biggest victory yet. Speaking to cheering supporters Tuesday night at Trump Tower, he declared: “We don’t have much of a race anymore.”

“[Texas] Senator [Ted] Cruz is just about mathematically eliminated,” Trump claimed. “We’re really, really rockin’.” Indeed, Cruz's poor showing left him with no mathematical chance of clinching the nomination before the Republican convention in July, though Trump could still end up short of the needed 1,237 needed to seal victory before the gathering.

With 94 percent of precincts reporting, Trump had garnered 60 percent of the vote, his highest total in any state. He had claimed at least 89 of New York's 95 Republican delegates.

Ohio Gov. John Kasich finished second in the state with 25 percent of the vote, leaving Cruz to finish third with 15 percent. Kasich was awarded at least three delegates, leaving Cruz in danger of getting shut out.

As of Tuesday night, Trump had 845 delegates. Cruz had 559, and Kasich had 147.

 

Cruz, who infamously panned Trump's "New York values" earlier in the primary, had been bracing for a tough showing in the Empire State and showed no signs of throwing in the towel. The Texas senator was already looking ahead, turning his attention to Pennsylvania, where he delivered a speech calling on Americans to join together to move the country forward.

"It is time for us to get up, shake it off and be who we were destined to be,” he said.

In the Democratic race, Clinton soundly defeated Vermont Sen. Bernie Sanders in her adopted home state, which she represented in the Senate for eight years. Despite the Brooklyn-born Sanders’ hard-fought attempt at an upset, the former secretary of state successfully staved off that possibility Tuesday night. With 94 percent of precincts reporting, Clinton had 58 percent to Sanders’ 42 percent.

“There’s no place like home,” Clinton said at her victory rally.

Clinton claimed the race for the Democratic nomination is now entering the “home stretch” and “victory is in sight.” In an apparent bid to bridge divides in the party amid an increasingly bitter primary, she directed a message to Sanders voters: “There is much more that unites us than divides us.”

Clinton and Trump both were seeking rebound victories Tuesday after recent setbacks. Cruz had complicated Trump's path to the nomination by winning recent contests like Wisconsin and getting allies elected to state delegate slates. On the Democratic side, Sanders had been on a winning streak up until Tuesday – winning seven of the eight prior contests. 

Whether Trump and Clinton's performance Tuesday will help either wrap up the race in the coming weeks remains an open question. The campaigns head next to five Eastern states that vote next Tuesday: Pennsylvania, Maryland, Connecticut, Rhode Island and Delaware.

It’s potentially friendly territory for the front-runners. But unless Trump can drive Kasich and Cruz out of the race, the billionaire businessman still may have to fight all the way to the final primary contests on June 7 – including delegate-rich California, which may end up being the deciding race – to see if he can clinch the nomination.

On the Democratic side, Clinton could easily attain the necessary 2,383 delegates to win by June. The question is whether Sanders would accept it – as her tally includes the support of party insiders known as “superdelegates,” and the Sanders campaign has suggested they shouldn’t count toward that 2,383-delegate threshold.

As of Wednesday morning, Clinton had 1,893 total delegates, compared with Sanders’ 1,180.

Sanders also campaigned in Pennsylvania Tuesday. He hammered his campaign themes about a “rigged” economy and “corrupt” campaign finance system, while urging voters to join him in challenging the status quo.

“We’re gonna win this election,” Sanders vowed. However, his senior adviser Tad Devine told the Associated Press that the campaign planned to "sit back and assess where we are" after a next week's contests.

According to an Associated Press tally, Clinton won at least 135 of New York's 247 delegates. Sanders had won 104, with eight delegates outstanding.

The importance of every last delegate has increased in recent weeks as Cruz has appeared to outmaneuver Trump’s campaign in the behind-the-scenes preparations for July’s convention.

Cruz has been laying the groundwork for a contested convention – one in which where no candidate has the required number of delegates – by getting allies elected as delegates. That way, if voting extends to a second round, some of those pledged to Trump on the first round could peel off and support Cruz. This has heightened the pressure on Trump to clinch the nomination before the convention. 

A Kasich campaign memo, meanwhile, touted the Ohio governor’s chances in the upcoming state contests – and his prospects for securing delegate support in the event of a contested convention.

“The next 7 days are absolutely critical," the memo concluded. "It’s now or never to stop Trump and save the Republican Party." 

The primary-day voting was not without its problems in New York. Voters ran into an array of polling-site glitches earlier Tuesday as they tried to cast ballots – with some locations opening late and others using broken machines.

The Wall Street Journal reported that some voters waited hours to cast ballots at a site in Brooklyn, where workers apparently did not have the keys when it was supposed to open Tuesday morning. Elsewhere in the borough, voters reportedly were turned away due to technical problems.

New York City Mayor Bill de Blasio also responded Tuesday to reports that thousands of registered Democrats have been dropped from the rolls, especially in Brooklyn. In a statement, the mayor called for major reforms to the election board and voiced support for an audit -- which the city comptroller has ordered.  

“It has been reported to us from voters and voting rights monitors that the voting lists in Brooklyn contain numerous errors, including the purging of entire buildings and blocks of voters from the voting lists,” he said in a statement. “I am calling on the Board of Election to reverse that purge and update the lists again …” 

The Associated Press contributed to this report.