The campaign of former President Donald J. Trump rejected criticism of his use of language, saying he would root out political opponents like “vermin” and doubling down by stating that the “sad, miserable existence” of those who made such comparisons would be “crushed” with Mr. Trump back in the White House.

Campaign spokesman Steven Cheung defended Trump’s remarks, dismissing critics as “snowflakes” suffering from “Trump Derangement Syndrome,” and stating that their “sad, miserable existence will be crushed when President Trump returns to the White House.”

Mr. Trump, at a campaign event in New Hampshire, vowed to “root out the communists, Marxists, fascists, and radical left thugs” and described his political opposition as the most pressing threat facing America.

However, some liberals and historians criticized Trump’s remarks, pointing to echoes of dehumanizing rhetoric wielded by fascist dictators like Hitler and Benito Mussolini.

A spokesman for President Biden’s re-election campaign also criticized Trump’s language, stating that Trump had “parroted the autocratic language” of dictators in his Veterans Day speech.

Mr. Trump’s speeches have grown more extreme as he tries to win a second term, with comparisons of immigrants to Hannibal Lecter and calling for shoplifters to be shot, drug dealers to face the death penalty, and insinuating that a military general appointed by him should be executed for treason.

Last month, Trump told a right-wing website that migrants were “poisoning the blood of our country,” language reminiscent of white supremacist ideology and comments made by Hitler in his manifesto “Mein Kampf.”