The Republican presidential candidate said, "I am a unifier. I would love to see the Republican party and everybody get together and unify. And there is no one who is going to beat us."
ABC News projects Trump will win the Georgia, Alabama, Massachusetts, Tennessee, Virginia, Vermont and Arkansas GOP primaries, based on exit poll data and vote analysis.
Trump said of the Republican party, "I think we're going to be more inclusive...more unified, and I think we're going to be a much bigger party. [The GOP] has become more dynamic. It's become more diverse. We're taking from the Democrats. I mean, look at South Carolina."
He added, "This is has been amazing evening...I want to congratulate [Cruz] on winning Texas, that was an excellent win. We are going to make America great again, folks."
Trump, who said his wife Melania and pregnant daughter Ivanka were in New York City, said, "We have a country that's in big trouble. Our infrastructure is going to hell. The middle class has been forgotten in this country."
Trump took the opportunity to bash Democratic presidential candidate Hillary Clinton. "We have to rebuild our country. Our country is going to hell...and Hillary Clinton doesn’t have a clue." He added, referring to Clinton's email scandal, "I don't know if she'll be allowed to run. What she did was criminal. If she is allowed to run it will be a sad day for this country because what she did is wrong. And other people have done far less than her and they paid a very, very high price."
Trump also spoke about his desire to be inclusive of women and minorities. "We're going to do great with African-Americans...I'm going to be really good for women. I'm going to be good for women's health issues."
And Trump brought up the wall he plans to build along the U.S.-Mexico border. "We are going to have a wall," he said. "100 percent, Mexico is going to pay. And the reason is, I know how to do this."
China also received an honorable mention. "I'm going to get Apple to start making their computers and their iPhones on our land, not in China."
As for Paul Ryan, Speaker of the U.S. House of Representatives, Trump said, "I don't know Paul Ryan well, but I hope to get along with him."
Trump, who owns a home in West Palm Beach, spoke on a stage lit with blue and red lights in the luxury golf resort's White and Gold Ballroom, which features ornate gold decorations lining the walls and ceiling.
Florida will hold its primary on March 15, although voting by mail and early voting is already under way.
Trump is the keynote speaker for the Palm Beach GOP at Mar-A-Lago on March 11.
A Quinnipiac poll of Florida Republican voters released last week showed Trump ahead of U.S. Senator Marco Rubio 44-28 percent.