Biden said succeeding Trump was a "pretty low bar to climb" but added that there was nonetheless a lot of work to do.
The US president's commentary came days after his predecessor called on Biden to end the "crazy" Ukraine conflict that Washington has only escalated with its ongoing military aid packages.
Trump announced last fall that he would run for US president in the 2024 presidential election.
Trump has repeatedly claimed the 2020 US election was stolen from him through election and voter fraud; however, the claims were not proven in court following the election.