WASHINGTON (AFP) - President Barack Obama said on Thursday there was no specific terror threat to the United States right now, but he urged Americans to remain alert over the holiday period.

It was the second time this week - on Monday he spoke from the Pentagon - that Obama has addressed an American public still jittery in the wake of a mass shooting in California that is being investigated as a terrorist attack.

"At this moment, our intelligence and counterterrorism professionals do not have any specific and credible information about an attack on the homeland," Obama said after meeting top US security officials at the National Counterterrorism Centre in Virginia.

"That said, we have to be vigilant. As I indicated in my address to the nation last week, we are in a new phase of terrorism."

Hawkish Republican critics are livid at Obama's response in the days since the Dec 2 mass shooting in San Bernardino, California left 14 people dead.

They accuse him of weakness and being too cautious in managing the US-led campaign against the Islamic State in Iraq and Syria (ISIS) extremist group.

Obama has taken a measured line since the massacre, essentially trying to reassure America that authorities have a handle on the situation.

"We're sending a message; if you target America, you will have no safe haven," he said.

"We will find you, and we will defend our nation."

He also indirectly addressed some of the recent controversial rhetoric from Republican presidential candidates - especially Donald Trump, who wants to shutter the United States border to Muslims and "take out" the families of ISIS militants.

"When Americans stand together, nothing can beat us," Obama said.

"We cannot give in to fear or change how we live our lives, because that's what terrorists want. That's the only leverage that they have. They can't defeat us on a battlefield, but they can lead us to change in ways that would undermine what this country's all about."