Joseph R. Biden Jr. increased his steady national lead over President Trump to 16 points in a poll released by CNN on Tuesday, another sign that Mr. Trump’s re-election chances were damaged by his debate performance last week.

The poll, conducted from last Thursday to Monday — entirely after the debate and mostly after Mr. Trump revealed he had contracted the coronavirus — showed Mr. Biden with the support of 57 percent of likely voters, and Mr. Trump with the backing of 41 percent. Eight percent of respondents said there was still a chance they might change their minds.

The winner of the November election is determined by how candidates perform in particular states and in the Electoral College. But national polls offer a broad view of the state of the race, and the CNN survey adds to a growing pile of evidence that Mr. Trump was, at the very least, unable to cut into Mr. Biden’s stable lead at the debate.

In CNN’s last national survey, conducted a month ago, Mr. Biden was up eight points among registered voters. A national poll conducted by The New York Times and Siena College in late September similarly had Mr. Biden ahead by 8 points among likely voters.

Polling after the chaotic debate has mostly shown Mr. Biden maintaining or expanding his lead. An NBC News/Wall Street Journal Survey released Sunday had Mr. Biden up 14 percentage points nationally.

The picture is no better for Mr. Trump at the state level. Times/Siena College surveys conducted after last week’s debate found Mr. Biden ahead by seven points among likely voters in Pennsylvania; five points among likely voters in Florida; and eight points in Arizona. Mr. Trump won all three states in 2016.

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