(CNN) -- Investigators think that as the San Bernardino, California, attack was happening, female shooter Tashfeen Malik posted a pledge of allegiance to ISIS leader Abu Bakr al-Baghdadi on Facebook, three U.S. officials familiar with the investigation told CNN.
Malik's post was made on an account with a different name, one U.S. official said. The officials did not explain how they knew Malik made the post.
A law enforcement official said it appeared that Wednesday's attack -- which left 14 people dead and 21 wounded before the two attackers, Malik and her husband, Syed Rizwan Farook, were killed in a shootout with police -- may have been inspired by ISIS. But none of the officials said that ISIS directed or ordered the attack.
"This is looking more and more like self-radicalization," a law enforcement official said.
Another official said authorities haven't ruled out that others may have influenced this radical view. In addition, the law enforcement source said investigators have a greater focus on whether the shooting occurred after a workplace issue with religion.
A lawyer for Farook's husband has said relatives have no idea why the couple burst into the holiday luncheon for Farook's co-workers and viciously opened fire. Nor did they have an idea the couple had a makeshift bomb lab in the apartment they shared with their 6-month-old daughter and Farook's mother. Nor did they know that either of them had become radicalized, as law enforcement officials have said.
"It just doesn't make sense for these two to be able to act like some kind of Bonnie and Clyde or something," Farook family attorney David S. Chesley told CNN's Chris Cuomo. "It's just ridiculous. It doesn't add up."
Farook occasionally went alone to shooting ranges, and he bought significant amounts of ammunition. But Chesley and fellow family lawyer Mohammad Abuershaid insisted those aren't red flags, nor are Farook's trips to Saudi Arabia -- first in 2013 for the Hajj, the annual pilgrimage to Mecca that Muslims are required to take at least once in their lifetime, then again to marry Malik, whom he'd met through an online dating service.
Farook and Malik "kept to themselves," Abuershaid said. But the interactions they did have didn't hint at any significant changes in their thinking or demeanor, any turn to Islamist extremism, or any sign they were plotting a mass killing, the lawyer said.
"There was nothing to show that (Malik) was extreme at all," Abuershaid said. "(And Farook) was a normal guy, in every sense of the word."
It's not that the family denies the couple carried out this massacre. They are shocked by it. And they're also "very remorseful and they're very sad."
But that doesn't mean they can explain it. And the shooters didn't make it easy for authorities either, given that the hard drive from their computer is gone, and two relatively new cell phones were found smashed in a garbage can near one of the crime scenes, law enforcement officials said.
Possible terror links
So far, officials have speculated that Farook's apparent radicalization may have been part of the reason. Part of it may have stemmed from workplace tensions. But they have declined to label this a terrorist attack.
"It would be irresponsible and premature for me to call this terrorism," FBI official David Bowdich said Thursday. "The FBI defines terrorism very specifically, and that is the big question for us: What is the motivation for this?"
Neither Farook nor his wife had gotten into trouble with the law. Neither was on any list of potentially radicalized people, and they had no clear ties to any overseas terrorist groups.
But investigators are exploring Farook's communications with at least one person who was being investigated for possible terror connections. Some were by phone, some on social media.
"These appear to be soft connections," an official said, meaning they were not frequent contacts. Farook's last communication with the contacts was months ago.
The FBI wants to interview some of them to learn more about their conversations with Farook.
A federal official said Farook has "overseas communications and associations," but it's not yet clear how relevant they are to the shootings. "We don't know yet what they mean," the official said.
Bowdich said that among other places, Farook had traveled to Pakistan, even though Abuershaid said "he never traveled to Pakistan."
The family lawyer says he thinks any focus on the shooters' Muslim faith is misplaced.
"(These) are isolated individuals (that) don't speak for the majority," he said. "The religion of Islam is a beautiful religion that would never ... agree with any type of killing like this. That is now what the religion is about: It is about peace, it is about love, it is about understanding. ...
"These aren't Muslim radicals. These aren't Muslims."
Was it a workplace dispute?
Could Farook's decision to attack the luncheon have stemmed from a religious dispute with a co-worker? His family lawyer's didn't speculate, though Chesley did say that "at some times co-workers have done silly things, like made fun of Syed's beard."
One of Farook's colleagues, Nicholas Thalasinos, liked to discuss religion and politics. He was one of the people killed in the Wednesday attack at Inland Regional Center.
Farook and Thalasinos, reportedly a devout Messianic Jew, once had a "heated, passionate" discussion, said Kuuleme Stephens, a friend of Thalasinos, who had called him at work.
The men were sticking by their strongly held positions but were not fighting, Stephens said.
Thalasinos' widow, Jennifer, said he was very verbal about terrorism. "He's very upset about what ISIS has been doing and the radicalized Muslims," she said.
Keeping quiet
Doyle Miller, Farook's landlord, said he had "no cause for concern" when he rented out a townhouse to him in Redlands.
"Everything checked out," Miller said. "He had good credit reports ... everything."
A religious leader who knew Farook described him as quiet.
"He's a little bit shy, a little bit withdrawn. He doesn't mix with people easily," said Mustafa Kuko, the director of the Islamic Center of Riverside where Farook was a regular until some time ago.
Farook's mother thought nothing of it when the couple asked her to watch the couple's 6-month-old girl while they went to a doctor's appointment, Abuershaid said. The lawyer didn't know if there ever was a doctor's appointment; only that the mother initially worried that Farook had gotten shot, not that he was doing the shooting.
The family -- who, Chesley said, has been "threatened and harassed" -- accepts the police account of what happened but still doesn't totally understand it. This includes the role of Malik, who her husband's relatives didn't know as well but didn't seem like someone who'd be involved in this.
"She's probably about 90 pounds, so it's unlikely she could even carry a weapon or wear some type of a vest or do any of this," Chesley said.
"There are a lot of things that just don't make sense."
Heartless killing
But the meek impression belied the heartless act Farook carried out with Malik.
First, at the luncheon, armed with .223-caliber long guns and with pistols, they fired 65 to 75 rounds, almost as many as there were people at the luncheon.
Later, in the shootout with police that killed them, they fired about the same number of rounds at officers. Two were injured in the gun battle.
In Farook's home, police found thousands of rounds of ammunition, 12 pipe bombs and hundreds of tools to make more explosives with.
The Farook family attorneys said that the possession of thousands of rounds of ammunition does not make someone a terrorist.
"When people have guns and they have ammo, a lot of times when they go shooting on firing ranges, they do waste a lot of ammo at these ranges," Abuershaid said.
But given the complete arsenal, police wondered if Farook and Malik were planning to kill many more and whether the luncheon was their original target. They say what they've found shows there was clear premeditation and planning.
CNN's Steve Almasy, Dave Alsup, Joshua Berlinger, Pamela Brown, Tina Burnside, Stella Chan, Deborah Feyerick, Joshua Gaynor, Faith Holland, Alberto Moya, John Newsome, Evan Perez, Andy Rose, Jim Sciutto, Catherine E. Shoichet and Barbara Starr contributed to this report.
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