The 46th US President was sworn in on Wednesday after his inauguration ceremony. Mr Biden has already signed 17 executive orders in his first few hours in office.
During a swearing-in ceremony for White House staff, President Biden told his employees he would fire them “on the spot” if they treat others with disrespect.
In a subtle dig towards former President Donald Trump, Mr Biden said “decency and dignity” had been missing from the previous administration.
He issued the warning to about 1,000 presidential appointees on a video conference after his inauguration.
The political aides will help President Biden steer his first term in the White House.
During the speech, Mr Biden said: “We have such an awful lot to do but I know you, I know your heart, your dedication, your commitment to this nation.
“And I know you can do it and we’re going to do it by leading with one core American value – humility, trust, collegiality, diversity, competency and family.
“I want to thank your families for the sacrifices.”
He then warned his White House staff against treating other colleagues with disrespect.
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President Biden asked his aides to help him correct any mistakes he may make during his time in office.
He said: “I’m going to make mistakes. When I make them, I’ll acknowledge them. And I’ll tell you.
“And I’ll need your help to help me correct them. We’re not going to walk away.
“We’re going to take responsibility. That’s what we do. That’s what you do.”
It came after Mr Biden became the 46th US President on Wednesday alongside Vice-President Kamala Harris.
Ms Harris made history as she became the first female, first Black and first South Asian Vice-President of the US.
Former President Donald Trump refused to attend Mr Biden’s inauguration ceremony.
He is the first President to snub a successor’s inauguration since 1869 and only the fourth President to have done so in US history.
However, Mr Trump’s Vice President Mike Pence did not follow in the former President’s footsteps and instead chose to attend Mr Biden’s inauguration.
In his inauguration speech Mr Biden promised to be a President “for all Americans” and will “fight as hard for those who did not support me as those who did”.