President Biden, prodded by Democrats to confront former President Donald J. Trump head-on about Mr. Trump’s criminal conviction in his New York hush-money case, heeded those calls on Monday night during a big-dollar fund-raiser in Connecticut for his re-election campaign and for the party.

Mr. Biden railed against his rival at a reception in Greenwich, telling a group of supporters who included Connecticut’s governor and its two sitting U.S. senators that the campaign had entered “unchartered territory” when a jury on Thursday found Mr. Trump guilty on all 34 felony counts that he had been facing.

He said Mr. Trump had cemented the distinction of being the first former president and convicted felon to seek the Oval Office.

“But as disturbing as that is, more damaging is the all-out assault Donald Trump is making on the American system of justice,” Mr. Biden said, according to a pool reporter covering the event.

Mr. Biden called Mr. Trump “unhinged” and said he was undermining another democratic institution with his vitriol after the verdict.

“It’s reckless and dangerous for anyone to say that’s rigged just because they don’t like the outcome,” he said.

A spokesman for Mr. Trump’s campaign did not immediately respond to a request for comment on Monday night.

Mr. Biden’s bluster at the reception, hosted by Richard Plepler, the former chief executive of HBO, was a notable shift in his approach to Mr. Trump’s conviction by a Manhattan jury.

When asked on Friday by reporters at the White House about the verdict, Mr. Biden grinned and walked away silently after making remarks about the war in Gaza. His reluctance to weigh in on the issue tracked with his general strategy to avoid personally engaging Mr. Trump about his legal woes.

Mr. Biden’s remarks at the fund-raiser echoed portions of a televised statement at the White House on Friday before he outlined his administration’s latest efforts to end the war between Israel and Hamas. Still, Democrats had called for him to be more aggressive.

Mr. Trump’s offender status was not the only line of attack for Mr. Biden during the fund-raiser.

Mr. Biden brought up the time when Mr. Trump suggested during a White House coronavirus briefing four years ago that bleach could be used to treat the disease, medical advice that was instantly debunked.

“He must have injected it into his brain,” Mr. Biden said, according to a pool report.