Speaking at an afternoon rally in Clear Lake, Trump said Cruz, who was born to an American mother in Canada and for most of his life retained dual citizenship, cannot claim that the matter is a "settled issue."
"You can't have a person running for office, even though Ted is very glib, and he goes out and says, 'Well, I'm a natural born citizen,' " Trump said. "The point is, you're not."
Trump also warned voters that legal challenges to Cruz's eligibility -- despite the views of most legal experts who say he is qualified to be commander in chief -- could be tied up in court for years. As he did earlier this week
, Trump offered Cruz some free legal advice.
"I say to Ted, as a Republican because I think it's very important, you gotta get it straightened out," Trump said, urging Cruz to seek a "declaratory judgment" from a judge so there's no doubt about his eligibility.
The real-estate mogul also pointed to Arizona Sen. John McCain, who also faced questions about his eligibility to be president. Trump said although the 2008 GOP presidential nominee was born in the Panama Canal Zone, his circumstances were distinct from Cruz's.
"The difference is his two parents were both in the military," Trump said. "What are you gonna do? Say, 'Mom and dad, you should have taken me back home to be born, I can't run for president?' He was born in a military base, and I understand that."
McCain himself commented on the issue earlier this week, calling Cruz's eligibility a legitimate question
Earlier Saturday, Trump said at a rally in Ottumwa that Cruz "has to straighten out his problems," a veiled reference to the so-called "birther" issue. But he declined to elaborate further, saying, "we'll discuss that later."
Speaking to reporters at the conclusion of his 28-county bus tour in Waverly, Iowa, on Saturday night, Cruz said candidates such as Trump are "dismayed" by his success in the polls and raising questions about his citizenship to avoid substantive debates about the future of the country.
"I recognize that there are candidates in the field that don't want to talk about those issues, and they want to instead encourage the good people of the media to go down rabbit trails and engage in silly sideshows," Cruz said. "I don't think the American people are interested."
But recently, Cruz has had to aggressively push back on Trump's questions about his eligibility for the presidency. He renounced his dual Canadian citizenship in 2014, and on Friday, Cruz's campaign shared with the conservative website Breitbart a copy of his mother's birth certificate
showing her born in the United States.
'Totally opposed to ethanol'
Trump is attacking Cruz on other fronts.
In Ottumwa, he took a swipe at the Texas senator over ethanol, saying Cruz -- who in the past has opposed federal subsidies for the corn-produced biofuel -- is only now claiming he's a friend of farmers.
"All of a sudden he was getting clobbered, and all of a sudden he said, 'Ah, oh, I'm for ethanol.' You can't do that. You can't do that with you know, three weeks to go, you're not allowed to do that. So, nobody really believes it," Trump said.
Cruz has said repeatedly he believes in leveling the playing field for the energy industry, calling to end mandates and subsidies for the ethanol and oil industries alike. He won ideological admirers when he attended a high-profile agricultural summit in Des Moines last year and refused to endorse the federal Renewable Fuel Standard
in front of an unfriendly crowd and has not shied away from his unpopular stance. But in recent days, he has tried to finesse the complicated politics
and is trying to focus voters' gaze toward his plans to roll back Environmental Protection Agency regulations on certain ethanol blends and to vigorously pursue antitrust cases to open up new markets.
And the Texas senator rejects Trump's claim that his positions on ethanol are based on donations from the oil industry, despite that most of his super PAC's anchor donors have made their money in the sector.
"It's factually inaccurate that the oil company's lobbyists are supporting me," Cruz told reporters Saturday night in Waverly. "The major oil companies and their lobbyists are not. They're supporting other candidates in this race. Those are the facts, and facts matter."
Trump raises questions among voters
In Clear Lake, however, Trump's attacks seemed to resonate among some voters.
Steve Ziller, a farmer from Belmond, Iowa, said he was "amazed" to learn that Cruz was born in Canada.
"I really did not know that he was from Canada. So that was new to me. I was not aware of that," said Ziller, adding that he agrees with Trump that this could raise questions about Cruz's eligibility to be president.
Ziller, who is undecided and leaning toward Trump but likes Cruz, also said he was aware of Trump's recent attacks on Cruz's stance on ethanol subsidies
. "Not very happy with that, to be honest. That's pretty big for the farm economy."
Dave Windmuller, a small-business owner from Mason City, said he personally doesn't question Cruz's eligibility to be president. Nevertheless, he said, it's now become a political liability that Cruz will have to quickly address.
"If there is any question, it should be addressed before the nomination," said Windmuller, who is likely to vote for either Trump or Cruz. "He should affirmatively do it before the nomination; otherwise, it's gong to be a cloud hanging over his head, and that will hurt him."