Mark Francois, MP for Rayleigh and Wickford, said Sir David had become “increasingly concerned" about the “toxic environment" that MPs were having to operate in and suggested a ban on social media anonymity to tackle the issue.
Sir David Amess was knifed to death in Leigh-on-sea on Friday while holding a constituency surgery. Ali Harbi Ali, 25, was arrested on suspicion of his murder and remains in custody.
Addressing the House of Commons during a series of tributes to Sir David on Monday, Mr Francois highlighted the vitriol faced by female MPs online, saying he was “appalled" by the “vile misogynistic abuse" directed towards elected officials on social media platforms such as Facebook and Twitter.
He told the House of Commons: “If the social media companies don’t want to help us drain the Twitter swamp, then let’s compel them to do it by law because they’ve had more than enough chances to do it voluntarily.
“Surely we can all agree that we came here to try for which we are now systematically vilified day after day… I suggest that if we want to ensure that our colleague didn’t die in vain, we collectively all of us pick up the baton, regardless of our party and take the forthcoming Online Harms Bill and toughen it up markedly.”
In response to the abuse, he urged MPs to “put David’s law onto the statute book”. Mr Francois conceded that “while people in public life must remain open to legitimate criticism”, they should “no longer be vilified or their families subject to the most horrendous abuse, especially from people who hide behind a cloak of anonymity with the connivance of the social media companies for profit.”
Mr Francois paid an emotional tribute to his colleague and friend, adding that he was "determined" to "not let him die in vain".
"Farewell my colleague, my great friend, in fact quite simply the best bloke I ever knew," he added.
Mr Francois' proposal comes as Home Secretary Priti Patel mulls whether to ban anonymous social media accounts amid concerns over the high volume of online abuse faced by MPs.
Asked whether she could introduce legislation to remove the right to anonymity on social media, Ms Patel told Sky News: “I want us to look at everything and there is work taking place already.
“I spend too much time with communities who have been under attack, who’ve had all sorts of postings put online and it’s a struggle to get those postings taken down. We want to make some big changes on that.”
However, shadow foreign secretary Lisa Nandy warned that removing online anonymity could threaten the work of pro-democracy campaigners in authoritarian countries who are likely to be persecuted for revealing their identity.
“We’ve got to get the balance right, because social media can be an enormous force," she said.
“You’ve got some incredible campaigners – the women of Belarus, the pro-democracy protesters in Hong Kong, the young people of Afghanistan – they’ve managed to use social media in order to make themselves heard."