President Biden on Tuesday denounced racist language at former President Donald J. Trump’s recent rally but appeared to insult Trump supporters as “garbage,” prompting waves of criticism from Republicans.

The White House quickly objected to that interpretation of the president’s remarks, arguing that he was instead describing the racist language as “garbage,” not Trump supporters.

The comments came as Mr. Biden was addressing Latino supporters by video. “Just the other day, a speaker at his rally called Puerto Rico a ‘floating island of garbage,’” Mr. Biden said, referring to a riff by Tony Hinchcliffe, a comedian and Trump supporter who spoke at the rally at Madison Square Garden on Sunday.

Mr. Biden said Puerto Ricans are “good, decent honorable people.” Then he went on: “The only garbage I see floating out there is his supporters — his, his demonization of Latinos is unconscionable, and it’s un-American.”