Speaker John Bercow and the Westminster political parties have agreed to “try to use moderate language”.
It comes after anger boiled over in the Commons during a debate last week on the PM’s suspension of Parliament.
The joint statement says those in leadership positions have a “duty to weigh their words carefully” given “stark divisions” over Brexit.
Signatories included government Chief Whip Mark Spencer and Labour leader Jeremy Corbyn.
The agreement was also signed by the SNP’s Westminster leader Ian Blackford, Lib Dem leader Jo Swinson, the DUP’s Nigel Dodds, Green MP Caroline Lucas, Change UK leader Anna Soubry, Plaid Cymru’s Liz Saville-Roberts, and Speaker John Bercow.
The statement says: “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.”
Speaking after a meeting with the Speaker and other political parties, Mr Corbyn said the rhetoric in the Commons needed to be “toned down” and urged MPs not to “use hyperbolic language which is dangerous”.
On Sunday Prime Minister Boris Johnson defended his choice of words saying he had been “a model of restraint” when it came to language around the Brexit debate.
Mr Johnson had been accused of dismissing concerns about death threats aimed at female MPs as “humbug” during a Commons debate.
He said there had been a “misunderstanding” over his intention – which he apologised for.
But he said he did not regret “using the word surrender to describe the surrender act” – after opposition MPs complained about his use of the term to describe the European Union (Withdrawal) (No 2) Act, which requires the PM to seek a Brexit extension.
“Military metaphors are old, standard, Parliamentary terms,” added the prime minister.