The Community Security Trust claims that society is entering "dangerous territory" as extremists are increasingly using newspaper websites to reach wider audiences.
Most newspapers, as well as broadcasters, have areas on their websites which provide open forums, allowing members of the public to create a blog or their own page.
The CST said this week that an increasingly large number of extremists were using such media outlets, giving them platforms with huge audiences through which to air their views.
One example is Richard Barnbook, the British National Party's London Assembly member, who has created a blog on the Daily Telegraph website, telegraph.co.uk.
Mark Gardner, director of communications at the CST, said: "Freedom of speech is not an absolute right where racists and extremists are concerned.
"It is important that responsible mainstream media outlets, such as the Daily Telegraph, take great care for whom they are providing a platform."
He stressed that Mr Barnbrook's blog was not an isolated trend and said that many newspapers and broadcasters such as The Guardian and the BBC had had their websites "utilised for the promotion of extremism and race hatred".
Although the CST is not calling for a ban on BNP representation in the media, it has said that when the party's supporters are given space in newspapers or on television, media outlets must ensure that readers and viewers are fully aware of who they are and the nature of their views.
Mr Gardner warned that this was a complex and growing issue which "society as a whole has not yet fully come to grips with" and said that policies needed to be implemented to deal with it.
"This is an issue that the CST has repeatedly flagged up in recent years and is something we have repeatedly raised in our conversations with MPs and government ministers," he said.
At The Guardian, the editor of the Comment Is Free section, Matt Seaton, said: "We have a zero-tolerance policy on antisemitic postings or any other form of hate speech.
"We devote considerable and growing resources to moderating out site, with the help of our users.
"We do not tolerate any hate speech, and our moderators will delete comments which are antisemitic or Islamophobic or otherwise racist , as soon as they are reported to us or when we see them ourselves. That happens in minutes rather than hours or days.
"We are very well aware that one should never be complacent about antisemitism in the public domain or other forms of racist discourse and we work very hard to tackle the issue and to keep racist commenting off our site."
A spokesman for the Telegraph Group declined to comment on Mr Barnbrook's blog posts.
A post on The Guardian's Comment Is Free section under the title "ItsAllLies" in July 2007 said: "Jewish people control the Western world. Of course they will use that control to get away with anything...That is what Jews are about. Taking control of people... If they did this back in 1940, no wonder Hitler started a war. Is that a bad thing to say? A man who saw his country taken over by a certain group of people who think only of themselves and screw everyone else, decides to take back his country and stop those people from using the countries around him to mount attacks on him? [sic]"
Posted on the BBC website by "Jamie, Croydon": "If you read the Protocols of the Elders of Zion you'll see plans for the domination of the entire Middle East by Zionists. Worried? We should all be, the plans are already afoot. Israel by its arrogance will drag us all into WWIII."
An anonymous writer left a post on the BBC website in July 2007 which read: "Zionism is a racist ideology where Jews are given supremacy over all other races and faiths... There is a law [sic] called Baba Mezia which allows Jews to lie as long as it's to non-Jews. Many pro-Jewish supporters will cringe at this being exposed because they know it exists, yet they keep quiet about it... The Law of Baba Mezia!! Tsk tsk tsk! It's in the Talmud [sic]."