Speaking on the final night of the Republican convention, the president depicted his opponent as "the destroyer of American greatness".
He said the Democrats would unleash "violent anarchists" upon US cities.
Mr Biden has a steady single-digit lead in opinion polls over Mr Trump with 68 days until voters return their verdict.
The end of the Republican convention heralds a 10-week sprint to election day, and the coming campaign is widely expected to be one of the ugliest in living memory.
On Thursday night, the president asked voters for another four years in office, vowing to dispel the coronavirus pandemic that has ravaged the US economy and quell civil strife ignited by police killings of African Americans.