Photo: Damon Winter/The New York Times; Video: By THE ASSOCIATED PRESS

PALM BEACH, Fla. — Basking in the glow of his Super Tuesday primary victories, an ebullient Donald Trump made his final appearance of the day in an ornate ballroom in his oceanfront Palm Beach home and vowed that he would be “a great president for the world.”

“This has been an amazing evening,” Mr. Trump said, going on to congratulate Senator Ted Cruz for his victory in Texas and calling Senator Marco Rubio a “little senator” whose recent broadsides against the New York businessman resembled a stand-up routine by the comedian Don Rickles.

Mr. Trump said that the forces arrayed against him in his own party would shower Mr. Rubio with millions of dollars in an effort to stop his march to the nomination, “but he’s not going to win anyway.”

It was clear from Mr. Trump’s remarks that he was making at least a token attempt at being conciliatory, particularly in the wake of accusations that his style is almost relentlessly divisive.

“I’m a unifier,” he told the crowd in the Small Ballroom, lit by three enormous chandeliers. “I know people are going to find that a little hard to believe.”

Shortly afterward, in response to a question about his views on Planned Parenthood, he said he was a “common-sense conservative,” noting that his only opposition to the organization lies in the fact that it provides abortions.

Mr. Trump noted also that he gives equal time to the three primary cable news networks, CNN, Fox News and MSNBC. “See?” he said. “I’m becoming diplomatic.”

Launching into a familiar tirade against politicians in general, calling them essentially all talk and no action, Mr. Trump seemed to catch himself by remembering that Gov. Chris Christie of New Jersey — who had introduced him — was standing right behind him. “Well, not Chris,” he said.

Mr. Trump’s 115-room mansion, Mar-a-Lago, the grandest of Palm Beach’s stately homes, was built by the cereal heiress Marjorie Merriweather Post on 17 acres in 1927. Mr. Trump purchased it in 1985, and a decade later turned it into a members-only country club.

On Tuesday night, Mr. Trump spoke from a small stage on which piano recitals and other forms of entertainment were performed in the glamorous days of Mrs. Post, once the wealthiest woman in the United States. Behind him stood 10 American flags, with a backdrop lighted in pink, peach and pale blue.

In the two front rows were friends and supporters of Mr. Trump’s, some of them members of a supporters’ group called The Trumpettes. The rest of the ornate Small Ballroom, with gold-leaf accents on the walls, columns and ceilings, was filled with reporters, television camera operators and photographers. Members of the public were not invited, so the occasion lacked much of the euphoria common to primary-night victory speeches, in which giddy supporters whoop and holler at the candidate’s every utterance.