In the Democratic race, Bernie Sanders scored a strong victory over Hillary Clinton in Wisconsin.
Donald Trump is still the frontrunner in the Republican field, but could fall short of the number of delegates needed to secure the party’s nomination.
His rivals have pinned their hopes on a contested convention.
At a contested convention, GOP leaders, not voters, would choose the nominee.
Donald Trump said on April 5 he would prevail despite the loss and took aim at his rival.
“Ted Cruz is worse than a puppet – he is a Trojan horse, being used by the party bosses attempting to steal the nomination,” the Trump campaign said in a statement.
GOP leaders are concerned that Donald Trump would be a weak candidate in the general election and could harm other Republicans lawmakers on the ballot.
Polls show that the real estate tycoon is extremely unpopular among key voting blocs including women, Latinos and young people.
On the Democratic side, Wisconsin adds to a recent spate of wins by Bernie Sanders campaign, giving the Vermont senator a boost before key races in New York and Pennsylvania.
Bernie Sanders won nearly every county in the state except Milwaukee, but as delegates are awarded proportionally he will not gain a significant advantage over Hillary Clinton.
Of the 86 Wisconsin delegates, Bernie Sanders is on course for at least 44, but Hillary Clinton will have at least 28.
Addressing supporters in Wyoming, which holds its primary on April 9, Bernie Sanders stressed momentum was on his side and that his outsider candidacy could change the status quo.
“Real change never takes place from the top down; it always takes place from the bottom up,” he told supporters.
Hillary Clinton still holds a sizeable lead and most analysts say she will eventually become the Democratic nominee despite her recent losses.
While Tuesday’s loss was a setback for Donald Trump, his campaign has time to rebound
The campaign now moves to large north-eastern states, where polls show Donald Trump holds significant leads.
Donald Trump’s loss in Wisconsin comes after a rocky week for the campaign, particularly with female voters.
He repeatedly struggled to articulate his position on abortion. At one point, he called for women to be punished for having abortions, then quickly changed his mind.
Meanwhile, outside groups opposed to Donald Trump’s nomination stepped up their efforts in Wisconsin, running negative television adverts.
Popular state leaders such as Governor Scott Walker and influential talk radio program hosts also opposed the Trump campaign and threw their support behind Ted Cruz.
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