During remarks at a New Hampshire rally on Veterans Day, Mr Trump pledged to “root out the communists, Marxist fascists and the radical thugs that live like vermin within the confines of our country” if he were to return to the White House.
In the same speech, Mr Trump said he would “implement strong and ideological screenings for all immigrants”, who he has previously said are “poisoning the blood of our country”.
Speaking at a campaign dinner in California on Monday night, Mr Biden said the Republican candidate's language was similar to that of the Nazis in the 1930s.
“It echoes language you heard in Nazi Germany in the ‘30s. And it isn’t even the first time,” Mr Biden said.
“Trump also recently talked about, quote, 'the blood of America is being poisoned' … Again, echoes the same phrases used in Nazi Germany.”
Mr Trump has historically used incendiary rhetoric to attack his opponents and others he perceives as enemies.
Steven Cheung, the Trump campaign spokesman, has rejected the comparison.
“Those who try to make that ridiculous assertion are clearly snowflakes grasping for anything because they are suffering from Trump Derangement Syndrome and their sad, miserable existence will be crushed when President Trump returns to the White House,” Reuters reported Mr Cheung as saying.
“Snowflake” is a derisory term conservatives use for liberals who are offended by right-wing or nationalist views.