Conservative Philip Davies, MP for Shipley, was encouraged by the Government to try to secure a parliamentary debate on the issue after voicing concerns in the Commons.
He highlighted comments from Ricky Gervais, which the comedian made following the hate crime conviction of a man who filmed and posted online a video of a pet dog giving Nazi salutes.
Mr Davies told Commons Leader Andrea Leadsom: “We guard our freedom of speech in this House very dearly indeed - something (Speaker John Bercow) rightly and robustly defends on our behalf - but we don’t often allow our constituents the same freedoms.
“Recent court cases have put the whole issue of freedom of speech into the public domain.
“Ricky Gervais and David Baddiel have joined forces on this issue.
“Ricky Gervais said ‘A man has been convicted in a UK court of making a joke that was deemed grossly offensive. If you don’t believe in a person’s right to say things you might find grossly offensive then you don’t believe in freedom of speech’.
“Can we have a debate about freedom of speech in this country - something this country has long held dear and is in danger of throwing away needlessly?”
Mrs Leadsom replied: “I absolutely commend (Mr Davies) for raising this very important issue.
“We do of course fully support free speech, however, there are limits to it and he will be aware there are laws around what you are allowed to say and I don’t know the circumstances of his specific point, but he may well wish to seek an adjournment debate to take this up directly with ministers.”
Conservative Sir David Amess (Southend West) earlier criticised “moronic cowards” who abuse others online.
He asked Mrs Leadsom: “Will you find time for debate on the regulation of social media? At the moment, people don’t have to leave their addresses when they post messages.
“Given the level of abuse and offensive messages, even when someone has died, isn’t it about time that these people were shown up for the moronic cowards which they are?”
Mrs Leadsom replied: “You make a very good point and also give a very good description of those who abuse others anonymously online.
“We expect all social media platforms to make it easy for users to choose not to receive anonymous posts.”
She added a social media code of practice to address bullying and insulting conduct would also be brought forward.