But "freedom is more powerful than fear," said President Obama, warning that falling prey to divisiveness in American society would play into the hands of extremists.
He also said the US must make it harder for potential attackers to obtain guns.
Mr Obama vowed that the US would overcome the evolving threat of terrorism, but warned that Americans "cannot turn against one another by letting this fight be defined as a war between America and Islam".
"If we`re to succeed in defeating terrorism, we must enlist Muslim communities as some of our strongest allies, rather than push them away through suspicion and hate," Mr Obama said.
He reminded his audience that Muslim-Americans were part of US society.
"And, yes, they are our men and women in uniform who are willing to die in defence of our country. We have to remember that," he said.
The president warned that turning against America`s Muslim communities would be exactly what Islamist extremists in the so-called Islamic State group want.
Mr Obama told Americans that terrorism had entered a new phase, from large scale attacks by al-Qaeda to less complicated attacks by radicalised individuals.
He said the US would draw upon "every aspect of American power" to combat IS.
He underscored that the US and its allies have increased their bombing of Islamic State oil infrastructure and would continue to train and equip moderate rebels in Iraq and Syria.
"Our military will continue to hunt down terrorist plotters in any country where it is necessary," he said.
The president added that there are a number of things that can be done on home soil to combat terrorism.
He called for stricter gun control and said he had ordered the Departments of State and Homeland Security to review the K-1 fiance visa programme under which the female attacker in San Bernardino originally entered the US.
This was only the third Oval Office address of Mr Obama`s presidency - they are reserved for events of national importance.
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