Websites should have protection from defamation cases if they act quickly to remove anonymous postings which prompt a complaint, a report says.
A joint parliamentary committee says it wants a "cultural shift" so that posts under pseudonyms are not considered "true, reliable or trustworthy".
It says websites which identify authors and publish complaints alongside comments should get legal protection.
But Mumsnet said the proposal could have a "chilling effect" on websites.
The report by the joint committee of MPs and peers who examined the draft defamation bill covers a wide range of defamation issues.
Its recommendations - including more protection for scientists and academics writing in peer-reviewed journals and more work on reducing "unacceptably" high costs of libel cases by encouraging more to be resolved through mediation - have been welcomed by the Libel Reform Campaign.
The committee also proposes a new "notice and takedown procedure" for defamatory online comments - aimed at providing a quick remedy for those who are defamed and to give websites which use the procedure more legal protection.
Under the current law, which the draft bill says needs to be clarified, websites risk being liable for defamatory statements made by their users if they pre-moderate comments or if they fail to take down a post when they receive a complaint.
The report says many "entirely legitimate" comments may be removed by websites who are keen to avoid legal liability.
It recommends that where complaints are made about comments from identified authors - the website should promptly publish a notice of the complaint alongside it.
The complainant can then apply to a court for a "takedown" order - which if granted, should result in the comment being removed, if the website is to avoid the risk of a defamation claim.
But where potentially defamatory comments are anonymous, the website should immediately remove them on receipt of a complaint, unless the author agrees to identify themselves, the report says.
'Mischievous and malicious'
The author of the comment can then be sued for defamation but if a website refuses to take down an anonymous remark it "should be treated as its publisher and face the risk of libel proceedings".
The report also says a website could apply to a court for a "leave-up" order - if it considers the anonymous comment to be on a matter of "significant" public interest.
The committee criticises comments made anonymously, which it says "may encourage free speech but it also discourages responsibility" and sets out moves it hopes will lead to a "cultural shift towards a general recognition that unidentified postings are not to be treated as true, reliable or trustworthy".
It says the aim of its proposal is to reduce damage "inflicted by the mischievous and the malicious".
But Mumsnet, a parenting website, says many of its members rely on the ability to ask questions or post comments anonymously.
Many of the women posting messages do so under a "user name", rather than their real name - and the site is worried the proposal will mean more people demanding messages be taken down.
Its co-founder, Justine Roberts, said while it was right to stop people from "assassinating the character of others from behind the cloak of anonymity" the report did not recognise how useful anonymous postings were "in allowing people to speak honestly about difficult real-life situations".
"The recommendations could have a chilling effect on sites like Mumsnet where many thousands of people use anonymity to confidentially seek and give advice about sensitive real-life situations."
In 2007, the website settled a libel case with Gina Ford, author of the Contented Little Babies book, over comments posted about her by its users.
A spokeswoman said they received about 10 complaints a month about comments on the site - and "two or three big ones a year" - often from small companies who had been reviewed by its members. It often agrees to take comments down.
But she said anonymous posts were important to the site - for example in its campaign for better care for women who have miscarried, where they have had a midwife and doctor making anonymous contributions.
"What we're really keen to do is to say there is some value in it [anonymous posts] and that is very different to being an anonymous troll and waging war on someone.
"If you think all anonymity is bad you could end up with unintended consequences of removing peer-to-peer support, in particular around sensitive issues."