Political leaders have vowed to tone down their language after an uproar in the House of Commons last week.
Labour leader Jeremy Corbyn - who is among those to have signed a cross-party statement on the matter - called on his colleagues not to use "hyperbolic language that's dangerous".
The Speaker of the House of Commons, John Bercow, is also among those to have signed the declaration after a meeting in Speaker's House in Parliament on Monday.
The Prime Minister rejected calls last week to temper his language, and said the best way to honour murdered MP Jo Cox, an ardent Remainer, was to "get Brexit done".
Boris Johnson had dismissed as "humbug" Labour MP Paula Sherriff's claim that like MP Mrs Cox, who was killed by a man with far-right sympathies just days before the 2016 referendum, many MPs faced death threats from people using the same sort of language as the Prime Minister.
The statement said: "We all accept that we have a responsibility to try to use moderate language.
"We all feel that those in leadership positions have a particular duty to weigh their words carefully, bearing in mind that there are stark divisions across the country on Brexit.
"The right of a member to personal safety is absolute and unconditional.
"Everyone is entitled to have a view - be they parliamentarian, journalist or a member of the public - and their right to safety cannot in any way be dependent on what that view is or the course of political action they take."
Signatories also include Westminster SNP leader Ian Blackford, Lib Dem leader Jo Swinson, the DUP's Nigel Dodds, former Green leader Caroline Lucas, Change UK leader Anna Soubry, Plaid Cymru's Liz Saville-Roberts, and Government chief whip Mark Spencer.
In an interview after the meeting with the Speaker, Mr Corbyn said: "This was a meeting that I requested last week after the Prime Minister made his statement to Parliament and the appalling language he used, particularly in respect of Paula Sheriff's comments over the death of Jo Cox.
"The Speaker agreed to host a meeting. We had it this morning with all party leaders there except Boris Johnson who was represented by the chief whip (Mark Spencer).
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"The Speaker has since drafted up a statement on behalf of us, which is to say, 'Tone down the rhetoric, tone down the language'.
"'Yes - political debate, yes - political disagreement, yes - passionate political thought but don't use hyperbolic language that's dangerous. Don't use language that incites people to act in a dangerous way on the streets of our country'.
"Surely we are an advanced democracy we can have a public discourse and public debate without resorting to the use without encouraging what becomes dangerous often racist activity on the streets of our country."
