But the Trump campaign had not yet committed to the event, Mr. Fahrenkopf said.
The contretemps may pose the most significant test to the debate commission’s legitimacy since the group, a nonpartisan body, was founded in 1987.
No law requires presidential candidates to take part in debates. Traditions and norms govern the practice, and like many political institutions in recent years, the commission’s board now faces its own Trumpian stress test.
Newton N. Minow, 94, a member of the commission who has been involved in every general-election debate since 1960, said on Thursday that the day’s developments amounted to “a big loss to the democratic process.”
“American voters are the losers — deprived of the opportunity to see, hear and evaluate presidential candidates through today’s technology,” Mr. Minow, who was appointed chairman of the Federal Communications Commission by President John F. Kennedy in 1961, wrote in an email.
Directors of the debate commission include former senators, business luminaries and the Rev. John I. Jenkins, the president of the University of Notre Dame, who tested positive for the coronavirus last week.
The commission was already under pressure to change its safety protocols after last week’s debate in Cleveland, where Mr. Trump’s family and aides declined to wear masks in the debate hall, flouting regulations set by the organizers. Mr. Biden’s aides had expressed concern about their candidate’s potential exposure to a president who could still be infectious.
Mr. Trump, in a Fox Business interview on Thursday shortly after he learned of the change to a virtual format, sought repeatedly to undermine the integrity of the debate commission. With no evidence, he accused the scheduled moderator of the next debate, Steve Scully of C-SPAN, of being a “never Trumper.” He said the moderator of the first debate, Chris Wallace of Fox News, “was a disaster” who favored Mr. Biden. And he said the commission’s plan for a remote matchup was about “trying to protect Biden.”