Andhra Pradesh Governor ND Tiwari on Friday denied media reports alleging his involvement in a sex scandal and termed them "malicious" even as women's groups held demonstrations outside his official residence here demanding his resignation. The opposition Telugu Desam Party (TDP) leader N Chandrababu Naidu has also sought the 86-year-old Tiwari's resignation for "unbecoming conduct". Ravi Shankar, Tiwari's lawyer told CNN-IBN news channel that the allegations were "a tissue of lies" and they had slapped a legal notice on the media house that telecast clips purportedly showing the governor in compromising position along with three young women in his bedroom.

Source : http://www.hindustantimes.com/hyderabad/Andhra-Governor-ND-Tiwari-denies-involvement-in-sex-scand...

Could you please explain to me what "even as" means in this context?
Yes, I go along. At the very same time as = even as.
When the Governor termed them as "malicious" , exactly at this moment,women's groups held demonstrations outside his official residence....
 Fandorin's reply was promoted to an answer.