“There will be a group that is in excess of six or seven people that I look at, because those background checks matter,” said Mr. Biden, who has gone through the process himself. He expressed hope that “once I pick someone, God willing if I’m the nominee, that there’s not going to be any snafu.”

Mr. Biden’s remaining opponent in the primary race, Senator Bernie Sanders of Vermont, has also shifted to campaigning virtually. Mr. Sanders held a live-streamed event on the coronavirus from Burlington, Vt., on Sunday, one of several such events he has done in recent days.

Since in-person campaigning came to a halt, Mr. Biden and his team have weighed in repeatedly about the coronavirus, sharply criticizing Mr. Trump’s handling of the crisis. But he has struggled to break through given the flood of news about the outbreak, and he lacks the kind of platform that is available to Mr. Trump, who has appeared daily at White House briefings on the virus.

Mr. Biden gave a speech about the coronavirus this month and released a plan for responding to the outbreak, and on Friday’s conference call with reporters, he urged the president to “stop saying false things.” But in the past week, he has been largely out of sight even as his campaign presses its case against Mr. Trump over his handling of the crisis.

Mr. Biden’s team has issued a number of written statements and has posted repeatedly on social media about the subject. His campaign released a video in which Ronald Klain, a former chief of staff to Mr. Biden who served as the Ebola response coordinator in the Obama White House, stands in front of a white board and discusses Mr. Trump’s handling of the virus and how Mr. Biden would respond. The video has now been seen four million times on Twitter.

Another video from the Biden campaign alternates between playing footage of Mr. Trump and Mr. Biden speaking about the coronavirus. “This moment calls for a president,” the video says at the end. “In November, you can elect one.”

A spokesman for the Trump campaign, Matt Wolking, on Sunday accused Mr. Biden of seeking to use the coronavirus for “political gain at the exact moment the country needs optimism and unity.”