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Riding high after big wins on Super Tuesday, Hillary Clinton returned to New York on Wednesday and shifted her attention to the Republican front-runner she could face in a general election: Donald J. Trump.

Mrs. Clinton made only glancing references to Senator Bernie Sanders of Vermont, her opponent for the Democratic nomination, and did not mention his name during an evening rally at the Javits Center in Manhattan. Instead, she focused on the coarse language coming out of the Republican primary fight and positioned herself as an optimistic antidote to Mr. Trump.

“I believe we need more love and kindness in our country right now,” Mrs. Clinton said to the cheering audience filled with union workers. “It’s always easier to tear people down than to build people up.”

Mrs. Clinton did not mention Mr. Trump by name either, but it was obvious that she has been paying close attention to him. Invoking his campaign slogan and signature policy, she said that America did not need to be made great again and that the country should not be dividing people with walls.

“There has been a lot of finger-pointing and insults going on over there in their primary,” Mrs. Clinton said. “Now maybe people think that’s entertaining, but I tell you, this is serious business.”

The level of discourse among Republican presidential contenders has devolved of late. In the last week, Mr. Trump and Senator Marco Rubio have unleashed a series of schoolyard-style attacks, mocking each other over perspiration, urination and hand size.

The former secretary of state has not been amused.

“It really matters when you’re running for president what you say,” Mrs. Clinton said. “And boy, does it matter when you are the president, about what you say when the whole rest of the world hears you.”

Mrs. Clinton continues to face a competitive race with Mr. Sanders, who is well-funded and has an enthusiastic following. But after winning several states and widening her delegate lead on Tuesday, she is emboldened.

“Boy, am I glad it worked out so well,” she said. “Yesterday was one for the history books.”

