While a second said: “Puppet masters always talk to their puppets.”
A third commented: “So Psaki just confirmed that it’s an Obama proxy presidency.
“With joe as the puppet.”
A fourth joked: “Awesome. Doubling down on the incompetence.”
However, Mr Biden and Mr Obama had their supporters as well, with one tweeting: “Two best Presidents ever!!!!!”
Earlier on Thursday, the 46th US President announced new measures to tackle gun violence, after a recent spate of mass shootings.
This will empower local courts and police forces to confiscate guns from those deemed a risk to their communities.
Mr Biden described gun violence in the country as an “epidemic” and “an international embarrassment” that had to stop.