Washington has often accused China of being behind US cyber-attacks.
But Mr Snowden has disclosed extensive gathering of phone and internet data by US agencies.
His latest revelations, published in the South China Morning Post, suggest a Beijing University was targeted.
He alleged that as recently as January this year the NSA hacked into computers and servers at the prestigious Tsinghua University in Beijing.
Mr Snowden is reported as telling the paper that on one single day in January, at least 63 computers and servers at the university were affected. »
In a commentary, it said the US had turned out to be the "biggest villain in our age".