U.S. President Barack Obama speaks about counter-terrorism and the United States fight against Islamic State during an address to the nation from the Oval Office of the White House in Washington, December 6, 2015. REUTERS/Saul Loeb/Pool

President Barack Obama vowed on Sunday to hunt down anyone plotting militant attacks against the United States as he sought to reassure Americans after a deadly California shooting rampage that has raised new questions about U.S. 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.

“The threat from terrorism is real but we will overcome it,” Obama said in a nationally televised speech.

Obama spoke just four days after U.S.-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 FBI is investigating the paramilitary-style attack as inspired by Islamic State, which controls swaths of Syria and Iraq and has shown an expanded reach beyond its Middle East strongholds, including complicity in the Nov. 13 assaults in Paris that killed 130 people.

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

The Obama administration plans to seek greater cooperation from U.S. technology companies to help ferret out such apparently homegrown attack plots, which could rekindle a privacy-versus-security debate between the government and Silicon Valley.

Even so, Obama cautioned against over reaction to the terrorism threat at home.

“We cannot turn against each other by letting this fight be defined as a war between America and Islam,” he said, alluding to the incendiary rhetoric by Republican presidential candidates like Donald Trump, which is seen by critics as fear-mongering against the Muslim community.

Given that the California couple were not on the U.S. national security radar before they launched their shooting spree on Wednesday, Obama faced the challenge of convincing the U.S. public he is doing everything possible to deal with an evolving militant threat.

There was mounting evidence that the pair were “lone wolf” assailants who may have become radicalized by Islamic State propaganda and then acted independently, making it all the more difficult for authorities to track them.

Obama’s address came amid growing pressure from Republicans and even some Democrats for a tougher response to Islamic State now that the San Bernardino shootings have raised fears among Americans about the threat of more attacks at home.

Last week’s massacre, if proven to be linked to or motivated by foreign Islamist militancy, would be the deadliest such incident on U.S. soil on Obama’s watch and since the Sept. 11, 2001, attacks on New York and Washington.