Malia Bouattia, 28, told a debate last night that those travelling to the war-torn country to join groups fighting there "feel so disempowered they're left with no choice".
Mass unemployment and the closure of youth centres had worsened their desperation, she added.
In audio obtained by The Huffington Post UK, Bouattia is heard telling the Bindmans UCL Faculty of Laws debate: "To answer the question around what is leading people to taking certain actions and joining these groups and wanting to inflict violence, I’d say it surrounds the political climate which we’re in.
"We need to start asking why people feel so desperate that they have to take such actions that they’re not necessarily in a space where such ideas are harnessed or encouraged like in the education system, we might say.
I'd also say we have to look at.. the fact that education is being privatised and rendered ever inaccessible
"What is leading particularly young people to feel so kind of disempowered that they’re left with no choice but to go off to Syria or join certain groups?
"And I’d also say we have to look at mass unemployment, the fact that education is being privatised and rendered ever inaccessible, youth centres have been closed down, every service available to support young people to allow space for critical thought and development has been shut down by the state.
...every service available to support young people to allow space for critical thought and development has been shut down by the state.
"Further to that our foreign policy and the space in which we would discuss and be critical of through the prevent strategy are being monitored and ever watched so that even the utterance of dissent is being policed and criminalise.
"If you want to look at the problem you have to look at the state’s hand."
Listen to her response, below.
Student groups said Bouattia's comments "misunderstand the problem".
Gray Sergeant, National Organiser at Student Rights, told HuffPost UK: "Claiming the privatisation of education and service cuts are responsible for radicalisation misunderstands the problem entirely, and downplays the damaging influence of extremist ideologies on vulnerable people.
"There are many pathways into violent extremism and Prevent aims to identify those at risk before they put themselves or others in harms way.
"This is a vital safeguarding effort and it’s high time the NUS stopped undermining those seeking to deliver the strategy."
The UCL debate was discussing Prevent anti-terror legislation, which forms part of the government's Contest anti-terror strategy.
Prevent has been controversial in recent months after the government enforced a "duty" on educators and school staff to observe and report those feared to be vulnerable to radicalisation.
Earlier this year, the National Union of Teachers condemned the plans.
Prevent has also been criticised in the past for unfairly targeting Muslim youths and students.
It comes after Julius Weinberg, head of Kingston University, said vice-chancellors were accepting the “counter-productive” anti-terror legislation in fear of being labelled extremist sympathisers by the media.
Bouattia, the first Muslim woman to become NUS president in the organisation's history, became leader in a closely-fought election in April.
She appeared on the UCL panel alongside David Anderson, the UK independent reviewer of terror legislation, Simon Cole, the chief constable of Leicestershire Police and Miqaad Versi, of the Muslim Council of Great Britain.
Bouattia used her opening speech at the debate to rally against Prevent.
"No-one here I trust will deny that Prevent is divisive, with a gulf between government and communities growing even wider on the issue," she said. "Prevent relies on ambiguity and public anxiety."
"Prevent is not just toxic it is corrosive," she added.
Bouattia stoked controversy in 2014 when she voted down a motion condemning Islamic State in a row over wording.