The court session was merely ceremonial. Kagan and the rest of the court will return Monday for the start of the new term.
In August, the 50-year-old New Yorker became the third woman on the current court, and its fourth ever. She replaced Justice John Paul Stevens.
Kagan took the oath again Friday in a ceremony by which the court formally welcomes its newest member. She wore a black robe she received as a gift from her former colleagues at the University of Chicago and Harvard Law School, where she served as dean, and a white scarf.
"We wish you a long and happy career in our common calling," Chief Justice John Roberts said after administering the oath.
Stevens and the other two living retired justices, Sandra Day O'Connor and David Souter, sat with Obama during the brief ceremony.
It was Obama's first appearance with the justices as a group since he criticized the court's campaign finance decision at his State of the Union speech in January.
Roberts formally greeted Obama, saying, "You are always welcome here."
After the court session, again following custom, Kagan and Roberts descended the steps in front of the court to pose for photographers.
Asked if she is ready for Monday, Kagan said, "All set."