David Baddiel has urged social media companies to do more to acknowledge that antisemitism is as important as other forms of racism.
The comedian, who clashed with former MP George Galloway on Twitter last week, was speaking at an event in Parliament discussing the balance between free speech and hate speech online.
Mr Baddiel said that his own response to internet abuse was to "mock the trolls" or make fun of their remarks, but acknowledged the problems faced by other users due to the ways different companies attempted to tackle the problem.
"The firms need to be very careful about logical inconsistencies," he said. "If they are going to have a policy it has to be logical."
The event was organised by the Antisemitism Policy Trust and introduced by John Mann MP, chair of the All Party Parliamentary Group Against Antisemitism.
Mr Mann said his appearance on the BBC's Question Time programme last week had sparked a torrent of abusive comments on social media, including threats of rape against his wife and of attack against his daughter.
Karim Palant, Facebook's UK Public Policy Manager, acknowledged the firm "has to have systems in place to get the bad stuff taken down". He said Facebook had doubled the number of staff members employed to investigate reports of abuse and was investing heavily in artificial intelligence aimed at highlighting offensive comments.
But he said "big conceptual decisions" about freedom of speech could not be left to private companies and called for a greater debate in society about the issues.
Dave Rich, the Community Security Trust's Head of Policy, said: "There has been progress in recent years.
"But I don't think we are asking Facebook and other platforms to be the ultimate arbiter of free speech. Facebook has the power to say it does not want Holocaust denial on its platform."
His point was backed by Karen Pollock, chief executive of the Holocaust Educational Trust, who cited an example of the daughter of a Shoah survivor having her Facebook account suspended after attempting to rebut a Holocaust denier with images from concentration camps.
Ms Pollock said Facebook needs to "get their heads around the fact that Holocaust denial is a form of antisemitism".
The well-attended event also heard from Baljit Ubhey, director of prosecution policy at the Crown Prosecution Service, who discussed the evidential thresholds needed to take action against those accused of grossly offensive comments.
She said context was important and each case had to be assessed on its own facts. This provided a "real challenge" which the CPS was working to meet.
Prosecutions for malicious communications had increased by 68 per cent in 2016-17, she said, bringing the number of convictions to more than 3,000.
Laura Marks, chair of the Holocaust Memorial Day Trust, said Facebook was "well positioned to do something" about abuse on its platform. Research for HMDT had revealed 85 per cent of people felt social media companies were responsible and should do more to tackle the problem, she said.