Obama then raised his right hand and placing his left hand on a bible, which has been in Michelle Obama's family for long, repeated the oath of office after Robert, who then congratulated the president. Obama then hugged his wife and daughters before they all went out together.
Since Jan 20, the designated inauguration day in the Constitution happens to be a Sunday, he will take the oath again Monday on the steps of the Capitol's West front with all the pomp and ceremony watched by some 800,000 people now converging on the capital.
Ronald Reagan was the last president to do the same, for his second inauguration in 1985. Before him Dwight D. Eisenhower did so in his second term in 1957.
Obama Sunday joined not only the fraternity of 21 second-term presidents, but the even more exclusive group of seven presidents whose inaugurations have fallen on a Sunday.
Earlier, Vice President Joe Biden was sworn in for his second term by Supreme Court Justice Sonia Sotomayor shortly after 8 a.m. at the Naval Observatory, his official residence.
Obama and Biden then travelled to Arlington National Cemetery before Obama's own swearing in at the White House.
The nation's first African-American president is expected to lay out the values and vision for his second term in his inaugural address before joining the traditional parade up Pennsylvania Avenue to the White House.
For Monday's public ceremony, less than half of the estimated 1.8 million onlookers who crammed the Mall in 2009 are expected.
The three million strong Indian-American community was among the first to begin the celebrations with what was billed as "Indiaspora 2013 Inaugural Ball" Saturday night.
Obama was not there, but his maternal half-sister Maya Soetoro-Ng, who came to cheer with Indian-Americans, called it "a reflection of how important India is and how important Indian-Americans are to the fabric of the nation".
(Arun Kumar can be contacted at arun.kumar@ians.in)
