Bernie Sanders won on Saturday in Nebraska and Kansas in the Democratic race, while front-runner Hillary Clinton took Louisiana, another divided verdict from the American people.
Mr Cruz, a Texas senator, claimed Kansas and Maine, and declared it “a manifestation of a real shift in momentum” while Mr Trump, still the front-runner in the hunt for delegates, took Louisiana and Kentucky.
In the overall race for Republican delegates, Mr Trump leads with at least 375 and Mr Cruz has at least 291, with Marco Rubio on 123 – It takes 1,237 delegates to win the Republican nomination for president.
Mrs Clinton has at least 1,117 delegates to Mr Sanders’ 477, including superdelegates – members of Congress, governors and party officials who can support the candidate of their choice. It takes 2,383 delegates to win the Democratic nomination. There were 109 at stake on Saturday.
Mr Cruz, a favourite of the ultraconservative tea party movement, attributed his strong showing to conservatives coalescing behind his candidacy.
With the Republican race in chaos, establishment figures are frantically looking for any way to derail Mr Trump, perhaps at a contested convention if no candidate can get enough delegates to lock up the nomination in advance. Party leaders – including 2012 nominee Mitt Romney and 2008 nominee Senator John McCain – are fearful a Trump victory would lead to a disastrous November election, with losses up and down the Republican ticket.
Mr Trump, at a post-election news conference in West Palm Beach, Florida, declared himself primed for a head-on contest with Mr Cruz, and called for Marco Rubio to drop out.
“I would like to take on Ted one-on-one,” he said, ticking off a list of big states where he said Mr Cruz had no chance. “That would be so much fun.”
Despite the support of many elected officials in Kansas, Florida Senator Rubio came up short, raising serious questions about his viability.