The Coalition Government is split over the Prime Minister's proposal to introduce a so-called "snooper's charter".
David Cameron said he would push for the legislation, which would give security services new powers to store and read the communications of internet users, after the terrorist attacks in Paris.
But the Deputy Prime Minister protested against the move and argued that privacy was a "qualified right".
"We do not make ourselves safer by making ourselves less free," Nick Clegg said.
The position puts the Liberal Democrat leader at odds with the party's Coalition Government partner and comes less than four months before the general election in May.
"Privacy is a qualified right. If someone wants to do us harm, we should be able to break their privacy and go after their communications," he told BBC Radio 4's Today Programme.
"But the snooper's charter was not about intercepting communications.
He added: "It was about storing a record of all your social media activity, of every website you have visited of every single individual in this country, of people who would never dream of doing anyone else any harm, would never dream of becoming a terrorist or having anything to do with extremist ideologies.
"The question we need to ask ourselves, in a free, open society as we defend our values against the abhorrent attacks we saw in Paris, is where do you draw the line?"
Cameron has ordered counter-terror police to be given extra training in how to deal with a Paris-style attack after the assault in France.
The Prime Minister warned that the UK must secure its defences against a "fanatical death cult of Islamist extremist violence".