But Director James Comey noted there’s still “a lot of evidence that doesn’t quite make sense”.
Syed Farook and Tashfeen Malik didn’t appear on the FBI’s “radar screen” before the shooting on Wednesday that killed 14 in San Bernardino, California, said Comey.
An IS-affiliated news agency Aamaq says the couple were “supporters” of the Islamic State group, but it stopped short of claiming responsibility for the attack.
The couple opened fire at a holiday banquet for Farook’s co-workers before dying in a gunbattle with police.
The FBI is treating the attack as an “act of terrorism”.
The couple attempted to destroy evidence, including crushing two mobile phones and discarding them in a rubbish bin, said David Bowdich, assistant director of the FBI’s Los Angeles office.
Malik praised the leader of the IS group in a Facebook post just minutes into the attack, a Facebook executive said.
A law enforcement official said Malik pledged allegiance to IS and its leader on Facebook, making her posts under an alias.
Facebook discovered the account on Thursday and removed the profile from public view.
Malik, 27, was a Pakistani who grew up in Saudi Arabia and came to the US in 2014 on a fiancee visa. Farook, a 28-year-old restaurant health inspector, was born in Chicago to Pakistani parents and raised in California.
Another US official said Malik expressed “admiration” for the extremist group’s leader on Facebook under the alias account. But there was no sign that anyone affiliated with the Islamic State communicated back with her.
The two US officials and the Facebook official asked not to be named.
Separately, a US intelligence official said Farook had been in contact with known Islamic extremists on social media.
Law enforcement officials have long warned that Americans acting in sympathy with Islamic extremists — though not on direct orders — could launch an attack inside the US. Using slick propaganda, IS in particular has urged sympathisers worldwide to commit violence in their countries.
Two weeks ago, with Americans on edge over the IS attacks in Paris that left 130 people dead, FBI director James Comey said that US authorities had no specific or credible intelligence pointing to an attack on American soil.
Seventy-one people have been charged in the US since March 2014 in connection with supporting ISIS, including 56 this year, according to a recent report.
Though most are men, “women are taking an increasingly prominent role in the jihadist world,” the report said.