Members of parliament are angling for stiffer rules concerning hate crime on social media, following publication of a cross-party report on antisemitism.

Written by an unofficial group of MPs and Lords, the document suggests that those who spread racial or religious hatred on sites such as Twitter and Facebook be banned from using the services, as is already the case with some sex offenders.

"There are innumerable benefits to be gleaned from social media but as the government set out in its recent paper on antisemitism, ‘protecting people from the harm caused by antisemitism on the internet remains a challenge’," the report said.

"The disparity of legal stances and global nature of the web means that the problem may never be fully resolved."

The legislators highlighted hashtag trends such as "Hitler Was Right" and "Kill the Jews" on Twitter as evidence of "cyber hate", noting that around a quarter of antisemitic incidents recorded by the Community Security Trust between July and August of last year occurred on social media, more than a tenfold increase from three years previously.

Nazi themes were said in the report to be present in Facebook comment chains concerning pro-Palestinian demostrations, the protests having been organised by groups such as the Palestine Solidarity Campaign, the Stop the War Coalition and the Campaign for Nuclear Disarmament.

However the report did not make clear whether such pages were under official control of the above organisations.

The report comes as Labour prepares to outline its own plans to quash hate crime online, amid criticisms from the opposition party that the government has been ineffective in its response.

"Much more needs to be done to tackle hate crime online," said shadow home secretary Yvette Cooper. "Too often industry has been slow to respond to reports of their social media platforms being used to bully and abuse people or spread abhorrent ideology."