The prime minister has been urged to apologise after he said the best way to honour Jo Cox, the MP murdered during the EU referendum campaign, was to "get Brexit done".
Boris Johnson was also criticised for calling the law aimed at blocking a no-deal Brexit the "surrender bill".
Labour MP Jess Phillips said the "bravest" thing for the prime minister to do would be to apologise.
But Tory chairman James Cleverly called criticism of the PM "deeply unfair".
During an ill-tempered debate on Wednesday, Mr Johnson was repeatedly challenged by opposition MPs over his use of the term "surrender bill" to describe legislation passed earlier this month, which aims to block a no-deal Brexit on 31 October if he fails to come up with a new exit deal with the EU before 19 October.
He dismissed one MP's intervention, in which she both criticised his use of language and mentioned the killing of Ms Cox, as "humbug".
Ms Cox, who supported Remain during the referendum campaign, died in 2016 after she was shot and stabbed in Birstall, West Yorkshire.
Her husband Brendan Cox told BBC Radio 4's Today programme he had been shocked by the language used in the Commons on Wednesday, saying Brexit debate had become a "bear pit of polarisation".
"I'm not sure that we can look the nation in the eye and say that was a good day."
That's how a Conservative MP has described the torrid scenes in the Commons in the last 24 hours.
Outrage is a common currency these days, but MPs' jaws dropped as Mr Johnson ramped up the rhetoric in responses to questions - suggesting first that it was "humbug" for a Labour MP to demand he temper his language, to try to protect MPs' safety.
Then, he went on to say that the appropriate legacy for the MP who was murdered during the referendum, Jo Cox, was for MPs to complete the Brexit process.
No surprise that Labour MPs howled in protest, some left the Commons in disbelief.
And there may be few Tory MPs willing, as the day goes on, to defend how far he went.
Asking an urgent question in the Commons on Thursday, Ms Phillips said: "The use of language yesterday and over the past few weeks such as the 'surrender bill', such as invoking the war, such as betrayal and treachery, it has clearly been tested, and workshopped and worked up and entirely designed to inflame hatred and division."
She added: "It is not sincere, it is totally planned, it is completely and utterly a strategy designed by somebody to harm and cause hatred in our country."
Ms Phillips also said: "When I hear of my friend Jo Cox's murder and the way that it has made me and my colleagues feel, and feel scared, described as humbug, I actually don't feel anger towards the prime minister, I feel pity for those of you who have to toe his line."
The "bravest and strongest thing" for Mr Johnson to do would be to apologise, she added.
Fellow Labour MP Paula Sherriff said she accepted it was "necessary for all us of to reflect" on the issue.
But, responding to MPs, Cabinet Office minister Kevin Foster said the government was working to ensure MPs "feel safe", especially online.
A Downing Street spokesman said: "The PM obviously made the broader point last night that he believes we need to get the issue of Brexit resolved because it was causing anxiety and ill-feeling in the country."
He added that, whatever their views, politicians and those in public life "shouldn't face threats or intimidation... it's completely unacceptable".
BBC political correspondent Chris Mason said Downing Street was not planning to shift away from using the term "surrender bill".
Meanwhile, the longest-serving male and female MPs, Ken Clarke and Harriet Harman, have called for an inquiry, chaired by Commons Speaker John Bercow, to discuss "protecting our democracy by guaranteeing the ability of MPs to go about their work without threat, harassment, violence or intimidation".
Rachel Johnson, the prime minister's sister, told BBC Radio 4's World at One that her brother was using the Commons as a "bully pulpit".
Ms Johnson, who stood for pro-European party Change UK - which has since altered its name to The Independent Group for Change - in June's European elections, added: "It's not the brother I see at home. It's a different person."
Conservative chairman Mr Cleverly said the debate over Brexit in the House of Commons had generated "a huge amount of temper on both sides".
"The best thing we can do to calm things down is to get it delivered, get it resolved," he added.
He also said the accusations levelled at the prime minister were "deeply unfair", adding that he had never described people as "traitors".
What questions do you have about MPs returning to Parliament, the Supreme Court's ruling and what happens now?
Use this form to ask your question:
If you are reading this page and can't see the form you will need to visit the mobile version of the BBC website to submit your question.