Additionally, the Better Business Bureau issued a statement disputing many of the New York billionaire's claims about a former business venture known as Trump University, currently the subject of fraud lawsuits.
"During the period when Trump University appeared to be active in the marketplace, BBB received multiple customer complaints about this business," the bureau said.
Complaints are automatically rolled off after three years, meaning that, over time as the school gradually ceased activity, Trump University's rating rose from a D-minus to an A-plus — the rating Trump has repeatedly cited during discussions of the episode.
"I'll win the lawsuit," Trump told reporters after the wins in Michigan and Mississippi.
The GOP front-runner also picked up a prominent endorsement ahead of Tuesday's primary: former New York City mayor Rudy Giuliani.
The run-up to Tuesday's delegate contests also included more in-fighting among Trump's opponents.
Rubio and his aides accused the Cruz campaign of spreading false rumors that the Florida senator is being urged to exit the race ahead of next week's Florida primary, where polls have Rubio trailing Trump. The allegations are similar to those that Ben Carson raised against Cruz on the night of the Feb. 1 Iowa caucuses.
The news report cited by Cruz backers and others is "a lie," Rubio told Fox News Radio, and "it looks like Ted Cruz’s campaign is putting out emails in places like Hawaii, telling people about it and you saw that with Ben Carson earlier.”
Cruz's aides said that volunteers in Hawaii sent out unauthorized messages about Rubio's prospects.
For his part, Cruz said he looks to maintain momentum he had on Saturday when he "clobbered" Trump in Kansas and Maine.
"The last election day — Super Saturday — was a very bad day for Donald," Cruz, a Texas senator, told reporters.
Meanwhile, Rubio and Kasich now face must-win primaries on March 15 in their home states to keep their campaigns afloat.
Those two candidates and Cruz argue that they are the best-positioned to defeat both Trump in the Republican race and likely Democratic nominee Hillary Clinton in the fall general election.
Rubio, addressing supporters Tuesday night, touted his credentials as a general election candidate, saying he can unite the party and defeat the Democrats in the fall, things he said Trump cannot do because too many Republicans find him to be an unacceptable nominee.
Saying that "I've been an underdog my whole life," Rubio told the crowd: "I believe with all my heart that the winner of the Florida primary next Tuesday will be the nominee of the Republican Party."
Kasich predicted he would start picking up more delegates as the race turned toward Ohio and other Midwest states. "Now the home-court advantage is coming North," he said. "And next week, we're going to win the great state of Ohio."
Trump also predicted success in Ohio and Florida, telling supporters that "I think we're going to clean the slate" and "I like to close things out."
Contributing: Chrissie Thompson, The Cincinnati Enquirer