WILMINGTON, Del. — Joseph R. Biden Jr. unloaded a barrage of criticism at President Trump on Tuesday over his response to Covid-19, his refusal to wear a mask, his handling of intelligence on Russia targeting American troops and even his “cognitive capability” during a rare news conference in which Mr. Biden repeatedly drew distinctions with his November opponent.

Mr. Biden, the presumptive Democratic nominee, laid out an updated plan to address the pandemic as cases rise in many states. He accused Mr. Trump of having “surrendered” to the virus. And he underscored the importance of wearing a mask in public, something the president has refused to do, saying, “You have a moral obligation.”

From a lectern in a high school gym in Wilmington, flanked by a pair of teleprompters and in front of an American flag, Mr. Biden laced into Mr. Trump in a 20-minute speech that focused on the coronavirus. Then he took questions from reporters for half an hour. The blistering critique he made of Mr. Trump spanned the breadth of the presidency, touching on matters foreign and domestic, as well as the tone Mr. Trump had set.

“I think we have to start appealing to the better side of human nature,” Mr. Biden said, making a case for wearing a mask. “It’s called patriotism. It’s called responsibility. It’s called making sure you look out for the other person.”

Mr. Trump, on the other hand, “puts everything in terms of him,” Mr. Biden said.

Before the speech, the Biden campaign released an updated plan for fighting the coronavirus, given “the current circumstances we face as a result of President Trump’s persistent failures.”

The plan said that “minutes after he is declared the winner of the election,” Mr. Biden would call Dr. Anthony S. Fauci, the nation’s top infectious disease expert, and ask him to work for Mr. Biden just as he has worked for past presidents.

“Dr. Fauci will have full access to the Oval Office and an uncensored platform to speak directly to the American people — whether delivering good news or bad,” the plan said.

The plan addresses issues like improving testing and tracing, supplying personal protective equipment, developing a vaccine and reopening the economy. In his speech, Mr. Biden encouraged the president “to adopt this plan in its entirety.”

Mr. Biden, the former vice president, has made only sporadic in-person appearances since the pandemic upended Americans’ daily routines, and his campaign is refraining from holding rallies with large crowds that are typically a staple of the campaign trail.

On Tuesday, Mr. Biden described the presidential race as “the most unusual campaign, I think, in modern history,” and he noted that he was not going to hold rallies — a contrast with Mr. Trump.

“I’m going to follow the docs’ orders, not just for me, but for the country,” Mr. Biden said.

“The irony is I think we’re probably communicating directly in detail with more people than we would have otherwise,” he said, describing his many virtual appearances and citing his strong poll numbers. “But I’d much rather be doing it in person.”

He has repeatedly criticized Mr. Trump over his response to the crisis, and this month, he laid out an eight-part plan for reopening the economy.

As of Tuesday, more than 126,000 people have died of the virus in the United States alone and more than 2.6 million people nationwide have been infected.

“Statewide lockdowns that so many Americans lived under for months were intended to buy us time to get our act together,” Mr. Biden said. “Instead of using that time to prepare ourselves, Donald Trump squandered it.”

His remarks came less than a week after he delivered a speech in Lancaster, Pa., in which he excoriated Mr. Trump for, among other things, having said at a rally that he had ordered a slowdown of coronavirus testing.

Concerns over the pandemic response have also spilled into the ongoing and fractious debate over health care. Mr. Biden has sought to draw sharp contrasts between his desire to expand health care coverage and the Trump administration’s legal effort to get the Affordable Care Act overturned.

Mr. Trump has staunchly defended his handling of the pandemic and has, at various times, claimed that the virus will fade away and that the spike in cases was a result of increased testing. He and his administration have insisted on reopening the economy rapidly, even as concerns about viral spread have persisted.

And the spike in cases in recent weeks in states like Florida, Texas and California has forced the political leaders of those states to pause their re-openings and close down businesses like bars that had previously been allowed to restart operations.

Katie Glueck contributed reporting.

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