"And put in another category, communications which are, as it were, merely offensive or grossly offensive."
He added: "[It] doesn't mean the second category are ring-fenced from prosecution, but it does I think enable us to think of that group in a slightly different way."
Social media sites may also be urged to improve moderation techniques to ensure that content that is deemed offensive is swiftly removed.
A freedom of information request has revealed that there were 2,347 investigations into offensive comments on social media sites in 2010. This then increased to 2,490 in 2011.