He said the killings were "an act of terrorism" designed to kill innocent people.
"Freedom is more powerful than fear," said President Obama, adding that divisiveness in American society played into the hands of extremists.
The FBI is investigating the mass shooting by a married couple that left 14 dead.
Syed Rizwan Farook, 28, and his wife Tashfeen Malik, 29, were killed in a shootout with police.
The president characterised the Islamic State (IS) militant group as "thugs and killers", adding: "The threat from terrorism is real, but we will overcome it."
The group said in a radio broadcast that the couple that carried out the attack were IS supporters, but gave no indication that IS was involved in its planning.
The FBI is also looking into reports Malik posted a message on Facebook pledging allegiance to IS around the time of the attacks.
This was only the third Oval Office address of his presidency - they are reserved for events of national importance.
President Obama has used Oval Office speeches sparingly, compared with previous presidents. His previous two addresses, both in 2010, covered the Deepwater Horizon oil spill and the end of combat operations in Iraq.
Other significant Oval Office addresses include:
- George W Bush following the 9/11 attacks of 2001
- Ronald Reagan on the Space Shuttle Challenger explosion in 1986
- Richard Nixon announcing his resignation in 1974
- John F Kennedy on the Cuban Missile Crisis in 1962
The Wall Street Journal says Mr Obama's use of the Oval speech to cover the terror threat "underscores how serious the issue has become for both the White House and the increasingly unsettled country".
FBI agents on Saturday raided a house in Riverside, California on a street where Farook used to live.
The home belongs to Enrique Marquez, a friend of Farook's who bought assault rifles used in the shooting but is not considered a suspect, US media reported.
Farook, who worked for the local health department, and Malik opened fire on an office Christmas party.
Their families have expressed astonishment at the attacks.
Farook's sister, Saira Khan, told CBS News: "I can never imagine my brother or my sister-in-law doing something like this, especially because they were happily married, they had a beautiful six-month-old daughter."
The couple used handguns and semi-automatic weapons that had been legally purchased in the US, police say.
Bomb equipment, weapons and thousands of rounds of ammunition were later found in their home.
It is the deadliest mass shooting in the US since 26 people were killed at a school in Connecticut in 2012.
The authorities said there was no indication so far the killers were part of an "organised group or formed part of a broader terrorist cell".
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