Biden and Trump appeal to their voters and address their weaknesses.

President Biden and Donald J. Trump are trying to defang some of the most damaging lines of attack against them, another sign that the tight campaign for president is intensifying as the country moves into the election year.

Mr. Biden on Thursday joined his two Democratic predecessors — Barack Obama and Bill Clinton — at a splashy New York City fund-raiser, where he assailed Mr. Trump’s ideas as “a little old and out of shape.” It was an effort to transform concerns on Mr. Biden’s age into an attack on his rival.

Earlier in the day, Mr. Trump used a visit with the family of a slain New York City police officer to lean into his tough-on-crime message, a twist for a candidate facing 88 felony charges.

The dueling events in the New York City area hinted at the campaign to come, where the full force of the Democratic Party establishment will face off against the passion of Mr. Trump’s MAGA movement.

Standing before a line of police officers in suburban Long Island, Mr. Trump, who is facing four criminal cases, including one in Manhattan that is going to trial in less than three weeks, proclaimed the need for the country to “get back to law and order.”

The three Democratic presidents sat for an interview on a celebrity podcast, were roasted by the actress Mindy Kaling, and interviewed by Stephen Colbert, a late-night host, before an audience of 5,000 donors. Their event raised $25 million, a record haul for a political fund-raiser.

Mr. Trump also continues to raise significant amounts of money, both for his campaign and his legal defense, using Mar-a-Lago, his Florida club and residence, as a base to host wealthy contributors.

At the Radio City event, the presidents were repeatedly interrupted by protesters, shouting “blood on your