In the ruling, head of Brazil's electoral court Alexandre de Moraes described the challenge as "offensive" to democratic norms, adding that it sought to encourage criminal and anti-democratic movements.
"I send my congratulations to Luiz Inacio Lula da Silva on his election to be the next president of Brazil following free, fair, and credible elections," Biden said in a statement.
Adding to tensions in Brazil, Bolsonaro has made baseless attacks on the integrity of Brazil's electronic voting system and suggested he may not concede if he loses.
The right-wing leader has threatened not to accept the results of next year's presidential election, which polls show him losing to left-wing ex-president Lula da Silva, if the system is not changed.