US President Barack Obama said today that Americans "have shown what it means to be strong in the face of terrorism" but urged them to stay vigilant, after last week's massacre of 14 people in San Bernardino, California, by a US-born Muslim man and his wife, a Pakistani national.

The FBI said the two had long been radicalized and conspired to commit terrorism without detection, underlining the challenge of finding so-called homegrown, self-radicalized extremists inspired by Islamic State propaganda.

In his weekly address, Obama pledged that he will review efforts across the entire US government to prevent attacks and protect the homeland.

Obama also reassured American Muslims that they are all "part of the same American family."

"Churches and synagogues are reaching out to local mosques, reminding us that we are all God's children," Obama said in his address.

"Grateful citizens are saying thank you to our patriotic Muslim American service members and veterans. Some of our greatest sports heroes have reminded us why they're true champions, and voices for tolerance and understanding. Across the country, Americans are reaching out to their Muslim friends, neighbors and coworkers, to let them know we're here for each other," Obama added.

Obama's comments came in the wake of a recent proposal from Republican presidential front-runner Donald Trump to ban Muslims from entering the United States.

Obama administration officials have said the fight against extremism requires the nation to build relationships with Muslims, not alienate them.