"I hate the idea of censorship but have seen for myself how dangerous inflammatory content on Facebook and Youtube can be," Omar wrote on microblogging site twitter.com.
His comments came hours after the Communication Minister Kapil Sibal expressed concern over objectionable content on social networking sites.
Making it clear that the government cannot allow this to go on, he has asked Internet firms like Google and Facebook to fall in line.
"I suggested that these platforms should evolve a mechanism on their own to ensure that such contents are removed as soon as they get to know of it...I have told them this cannot go on," Sibal told reporters in New Delhi today.
Omar said while he was staunch supporter of freedom of speech, those exercising this right should also take the responsibility that comes with it.
"If push came to shove I'd come down on the side of freedom of speech but it's one of those freedoms that has me worried unfortunately...We want the luxury of free speech but not the burden of responsibility for how we use that freedom. Something will have to give," the chief minister tweeted.
Omar's father and Union Minister Farooq Abdullah in a function here yesterday had also asked the media to tone down its reportage of protests in JK as it had a "negative impact" on the Tourism industry.