US Republican presidential candidates responded quickly on social media to President Barack Obama's televised address to reassure Americans after a deadly California shooting rampage that has raised new questions about US defenses against homegrown extremism.

In a rare Oval Office address, Obama tried to counter mounting criticism he has not acted decisively enough to keep the United States safe from the Islamic State militant group, but he stopped short of offering any major shift in his strategy.

Obama spoke just four days after US-born Syed Rizwan Farook, 28, and his Pakistani wife, Tashfeen Malik, 29, opened fire on a holiday party for civil servants in San Bernardino, California, killing 14 people. The pair were killed hours later in a shootout with police.

Obama condemned the attack as "an act of terrorism designed to kill innocent people," but also called it a "new phase" in the fight against Islamist militancy.

The candidates blasted the speech.

"It's 100 per cent wrong and proves the need for new leadership for our country. His administration is focused on gun laws that won't stop terrorists while pushing policies that will let more of them in the country. There are answers here to make our nation safe, but once again, the president seems incapable of finding them," Senator Rand Paul wrote on Twitter.

Billionaire Donald Trump tweeted: "Wish Obama would say ISIS, like almost everyone else, rather than ISIL. Is that all there is? We need a new president - fast!"

"Vintage Obama: No strategy, no leadership. Politics as usual," Carly Fiorina wrote.

"I will shut down the immigration system that is letting jihadists into our country," Senator Ted Cruz promised, if elected president.

"President Obama has finally been forced to abandon the political fantasy he has perpetuated for years that the threat of terrorism was receding. We need to remove the self-imposed constraints president Obama has placed on our intelligence community and military, and we need to put in place an aggressive strategy to defeat ISIS and radical islamic terrorism as i have proposed. Unfortunately, neither he nor Hillary Clinton has the resolve to put in place such a strategy," former Florida Governor Jeb Bush wrote on Facebook.

Speaker of the House Paul Ryan called the president's address "a half-hearted attempt to defend and distract from a failing policy".

The FBI is investigating the paramilitary-style attack as one inspired by Islamic State, which controls swaths of Syria and Iraq and has shown an expanded reach beyond its Middle East strongholds,

But Obama said there was no evidence the assault was directed by a militant group overseas or part of a broader conspiracy at home.

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