That possibility emerged late last week when it was disclosed that the Pakistani-born Malik had pledged allegiance to the Islamic State group in a Facebook post at about the same time she and husband Syed Farook launched the attack Wednesday that left 14 people dead at a holiday luncheon.
Britain's Sunday Times reported that Malik shot first during the attack while Farook, 28, appeared to "hesitate".
Federal investigators continued trying to establish what pushed the couple to carry out what appears to be the deadliest attack on American soil by Islamic extremists since 9/11.
"We're looking at everything we can find out about these two killers' lives - how they grew up, where they grew up, how they met. All of those things will provide us guidance."
Lynch said the FBI terrorism investigation so far has involved "over 300 interviews, several locations searched, a lot of information being processed, being analysed and being gathered, and more to come."
Separately, a law enforcement official said investigators were looking into whether Malik was radicalized in the Middle East, where she spent considerable time, and used her 2014 marriage to Farook to penetrate the US and commit jihad. But the official said it was only one among a number of theories being pursued.
The two officials were not authorised to discuss the investigation publicly and spoke on condition of anonymity.
While radical Islamic groups at times have mobilised women as suicide bombers, and jihadist women may exhort their men to attacks, it is extremely rare in conservative Muslim societies for female jihadists to take part in actual combat, as Malik did.
Malik, 29, and Farook, 28, were killed in a furious shootout with police hours after they opened fire with assault rifles on a gathering of Farook's colleagues from the San Bernardino County public health department, where he worked as a restaurant inspector.
Former classmate Afsheen Butt said Malik showed drastic changes after a trip to Saudi Arabia in late 2008 or early 2009.
"She used to tell us that this is the real life. We are a nation that has strayed from the right path," Butt said. "She used to give us Islamic religious literature."
Saudi Interior Ministry spokesman Major General Mansour Al-Turki said authorities there had received no indication Malik was radicalised in Saudi Arabia.
Pakistani Interior Minister Chaudhry Nisar Ali Khan said Sunday that investigators so far had found no evidence linking Malik to Islamic militants. He said his country was ready to share any information it has about Malik and her family.
"We have nothing to hide," he said.
Meanwhile, police took people into the parking lot of the Inland Regional Centre, where the attack occurred, to retrieve their cars, which had been stuck at the crime scene. Some people hugged as they waited to get into the police cars. One man wore a T-shirt with the logo "SB Strong."
