Malik, 29, a Pakistani national, pledged allegiance to the Islamic State group before she and her husband Syed Farook shot dead 14 people in California last week.
Investigators are trying to establish if she had contact with radicals while in Pakistan or in Saudi Arabia, where she is believed to have spent extended periods of time.
Malik studied at a university in the central Pakistani city of Multan from 2007-2012 and in 2013 formally enrolled in Al-Huda, one of the country's most high-profile religious seminaries for women.
Malik's attendance at the deeply conservative school, which was visited by counter-terror and intelligence officials yesterday, appears to offer fresh insight into her journey towards Islamic radicalism.
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The school today rejected any responsibility for the massacre, condemning such acts anywhere in the world.
Malik was a "hardworking, friendly, helping, obedient and positive-minded student", the institute said in a statement, expressing disbelief that she could "do such a horrible thing that is 100 per cent against Islam".
She enrolled in the Multan branch of the seminary on April 17, 2013, the statement said, and left on May 3, 2014 -- telling her teacher she was to be married in two months.
Al-Huda, founded in 1994 by Farhat Hashmi, mainly targets Pakistan's influential middle and upper-class women seeking to come closer to Islam.
A spokeswoman said today the organisation would now be "more careful" when admitting students, trying to assess both their purpose in joining and their mental state.
Pakistan has pledged to crack down on religious seminaries suspected of being breeding grounds for intolerance or even fostering extremism.