Republican presidential hopeful Ted Cruz said Wednesday that former Hewlett-Packard executive Carly Fiorina would be his vice presidential running mate if he wins the party's nomination, in a move that rival Donald Trump dismissed as a "waste of time."

Cruz pointed to Fiorina's climb up the corporate ladder from secretary to chief executive and called her an "extraordinary leader" who knows how to create jobs.

"Over and over again, Carly has shattered glass ceilings," Cruz said at a rally in Indianapolis, Indiana.

Cruz is seeking to prevent front-runner Donald Trump from securing the centre-right party's nomination for November elections and hopes pairing up with Fiorina, who ended her own presidential bid in February, will bolster his campaign.

Fiorina could appeal to the party's large traditional pro-business wing and as a political outsider to reach people fed up with politics as usual. As a woman, she is also in a position to counter Trump's sexist remarks and eventually to take on Hillary Clinton, who is seeking to become the country's first female president.

Fiorina lost a Senate bid in California in 2010 to long-time Senator Barbara Boxer, but her connections in the state could help Cruz in the primary there if he survives until the most populous US state votes on June 7 in the final round of Republican primaries.

Cruz noted the move to name a running mate was highly unusual at this stage in the campaign without having secured the nomination, but said he wanted to send a clear message and unite the party.

Trump called it a "waste of time" in a speech to supporters in Indianapolis.

"Cruz can't win. What's he doing picking vice president?" he said.

On Wednesday, Fiorina, who endorsed Cruz last month, declared that Trump and leading Democrat Clinton would both be "disastrous for this nation."

"This is a fight for the soul of our party and the future of our nation," said Fiorina who pointedly went head to head with Trump in early televised debates after he criticized her looks.

Trump won five primaries in north-eastern states Tuesday. He holds a formidable lead in the delegates needed to secure the party nomination at its convention in July but has yet to garner enough to definitively secure the nomination. Some in the party establishment who oppose Trump hope to deny him enough delegates to force a more open battle for the nomination at the convention.

Cruz, who himself is unpopular among the party establishment, has emerged as Trump's strongest challenger, but must have a strong showing in upcoming contests in order to stop Trump as the billionaire businessman gains momentum.

"Nobody is getting to 1,237 delegates," Cruz said, calling on voters to stand by his campaign despite the view of some that Trump is becoming the inevitable candidate. "I'm not getting to 1,237 delegates and Donald J Trump is not getting to 1,237 delegates."

The next contest is in the central state of Indiana on Tuesday and the primary is seen as a must win for Cruz. He and rival John Kasich earlier this week said they would divide their resources in upcoming contests to better take on Trump in states where each has a stronger shot.

After Tuesday's strong showing Trump said he considers himself the party's "presumptive nominee" and called on Cruz and Kasich to drop out of the race.

On the Democratic side meanwhile, Clinton won four of five contests Tuesday and her rival, Bernie Sanders, indicated Wednesday in an interview with the New York Times that he would lay off hundreds of campaign workers.

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