The girls, vocalist-guitarist Noma Nazir (16), drummer Farah Deeba and guitarist Aneeka Khalid (both 15), who defied convention to form the rock band "Pragaash" (darkness to light), have stopped live shows in the wake of the online threats.
Activists and artistes expressed outrage at the online hate campaign against the girls, all students of Class X.
"It is completely shameful...why is police silent against these cyber criminals.... Police chief should have initiated action against them and it should be done under the law of the land. Enough is enough," filmmaker Shaykhh Mukhtar said.
Activist Humaira Khan said "we are moving ahead, but why aren't our mentalities. We move ahead in real sense only when we open our minds."
The first live performance of Pragaash at Srinagar's music festival Battle of the Bands in December had created ripples in the Valley.
But their euphoria was short-lived as the girls soon started receiving online threats including to their lives and absurd comments, leaving their parents worried and forcing them to keep a low profile.
The Chief Minister said it was a matter of shame that those who demand freedom of speech on social media networks, use it to threaten the girls.
"The police will examine the threats issued and whether any provision of the law can be used to book those making the threats (to the rock band)," Mr Abdullah said, adding "I hope these talented young girls will not let a handful of morons silence them."
"Shame on those who claim freedom of speech via social media and then use that freedom to threaten girls who have the right to choose to sing," he wrote on Twitter.
Though there are dozens of bands currently playing popular music of different genres in the Valley, this is the first all-girls rock band and was among the winners after their maiden public appearance.
"There has been a wicked campaign against the girls ever since they made their maiden appearance in public on December 26," said Adnan Matoo, who runs musical academy Band Inn where the girls are undergoing training.
Mr Matoo, who is also the band manager, said the girls cried after seeing the abusive comments online. "I told them such things keep happening in the social media."
The girls have been accused of breaking traditions and bringing shame to the society. Though they have stopped the live shows for the time being, the girls said they would continue to pursue their passion-music.