"Privacy rulings affecting newspapers are "unsustainable" and unfair on the press, the prime minister has said.
David Cameron told ITV1's Daybreak the law should be reviewed to "catch up with how people consume media today".
"It comes after Scotland's Sunday Herald became the UK's first mainstream paper to name a footballer accused on Twitter of taking out a privacy injunction."
Twitter users had responded to a legal bid to find out who was behind messages naming a footballer by posting more.Situation 'unsustainable'
"The player, who an injunction says can only be identified as CTB, is involved in proceedings against ex-Big Brother contestant Imogen Thomas, who is a former Miss Wales, and the Sun newspaper.
Mr Cameron told Daybreak: "It is rather unsustainable, this situation, where newspapers can't print something that clearly everybody else is talking about."
"But there's a difficulty here because the law is the law and the judges must interpret what the law is.
"What I've said in the past is, the danger is that judgements are effectively writing a new law which is what Parliament is meant to do."