"Yes, Major nipped someone on a walk", Michael LaRosa, the first lady's spokesman, told CNN.
White House press secretary said the dogs returned to Biden's hometown as part of a "pre-planned trip" as First Lady Jill Biden was going to be away that week.
"Major is still adjusting to his new surroundings and he nipped someone while on a walk".
In an interview with ABC Newsearlier this month, Biden claimed that Major "did not bite someone and penetrate the skin" in the first incident, adding that "the dog's being trained now with our trainer at home in DE".
The German Shepherd only returned to the White House last week - along with his sibling Champ - after causing a minor injury to a member of the US Secret Service. Champ had already spent some time in the White House as a younger dog, when Mr Biden was vice-president, before moving in permanently in January this year. "Out of an abundance of caution, the individual was seen by [White House Medical Unit] and then returned to work without injury".
Among them was MSNBC's Joe Scarborough who, on his show Morning Joe on Tuesday, repeatedly suggested Major be sent to "dog Jesus".
The President said Major was being trained in DE but disputed the idea that the pup had been sent away after the incident.
"You turn a corner, and there's two people you don't know at all, and he moves to protect", Biden said. "Eighty-five percent of the people there love him".
The first dog went after a National Park Service employee, according to CNN.
'I didn't banish him to home. It was reported that Major had been undergoing training during his days away from the White House.
The dogs met the Bidens two weekends ago at Camp David in Maryland and came back to Washington on March 21.
The Bidens adopted Major, who is now three years old, as a puppy from Delaware Humane Association in 2018.
Major Biden jokes and memes began flowing on Twitter.