The Prime Minister has been widely condemned after he berated MPs, rejected calls to temper his language and said the best way to honour the late Mrs Cox - an ardent Remainer - was to "get Brexit done”.
He also dismissed as “humbug” Labour MP Paula Sherriff’s claim that like 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 copying the language used by the Prime Minister.
As the row spilled over into Thursday, Downing Street has declined to apologise for the Prime Minister's words in the Commons, while an urgent question was asked in Parliament about his language.
Commons Speaker John Bercow pleaded with parliamentarians on all sides to tackle the "toxic" political culture, and said the House "did itself no credit" in the angry exchanges which followed the Prime Minister's statement.
As MPs returned to the Commons on Thursday morning, Mr Bercow said: "There was an atmosphere in the chamber worse than any I've known in my 22 years in the House.
"On both sides passions were inflamed, angry words uttered, the culture was toxic."
Labour MP Jess 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 work-shopped and worked up and entirely designed to inflame hatred and division.
"I get it, it works, it is working."
She continued: "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 people opposite me know how appalling it was to describe the murder of my friend as mere humbug.
"I want to ask the Prime Minister to apologise and to tell him that the bravest, strongest thing to say is sorry - it will make him look good, it will not upset the people who want Brexit in this country if he acts for once like a statesman."
Labour leader Jeremy Corbyn warned that the words politicians use "have real consequences", adding: "To dismiss concerns from members about the death threats they receive and to dismiss concerns that the language by the Prime Minister is being repeated in those death threats is reprehensible.
"To dismiss those concerns in an abusive way as he did is completely unacceptable."
Tracey Brabin, who succeeded Mrs Cox as MP for Batley and Spen following her death in 2016, said Mr Johnson needed to remember "his words have consequences”.
"He just proved that he has no emotional intelligence, because then to say that the best thing we can do to remember Jo is 'to get Brexit done' when Jo was a passionate Remainer.
“Only the day before her tragic murder she was on the Thames with her family campaigning to stay in the EU - it just seemed extraordinary," Ms Brabin told BBC's Radio 5.
"It got gasps around the chamber, because remember that Jo worked cross-party - she had friends in all parties. And just the crassness of it was deeply shocking.”
Mr Corbyn said the PM's language "was indistinguishable from the far right", while his Liberal Democrats counterpart Jo Swinson said Mr Johnson's comments were "a disgrace”.
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"He heard the pleas of MPs, many of whom who have faced death threats, to moderate his language and dismissed their concerns with the same callous bluster that has become his trademark," Ms Swinson said.
Former cabinet minister Amber Rudd - who quit the Government and the Tory Party over Mr Johnson's approach to Brexit - told ITV's Peston programme the PM's remarks were "dishonest and dangerous".
Secretary of State for Digital, Culture, Media and Sport Nicky Morgan appeared to acknowledge concerns about Mr Johnson's use of language, particularly in the context of threats of violence against politicians.
"But at a time of strong feelings we all need to remind ourselves of the effect of everything we say on those watching us," she tweeted.
Boris Johnson's comments about Jo Cox and far right threats to MPs in Parliament tonight show once again why he is unfit to be Prime Minister.— Jeremy Corbyn (@jeremycorbyn) September 25, 2019
Feel a bit sick at Jo’s name being used in this way. The best way to honour Jo is for all of us (no matter our views) to stand up for what we believe in, passionately and with determination. But never to demonise the other side and always hold onto what we have in common.— Brendan Cox (@MrBrendanCox) September 25, 2019
Boris Johnson’s comments this evening were a total disgrace. He has demeaned the office of Prime Minister and he should apologise for them immediately. https://t.co/7ZBWw2iw4h— Jo Swinson (@joswinson) September 25, 2019
.@AmberRuddHR calls Boris Johnson “dishonest and dangerous” after he described @paulasherriff's complaint about his language as “humbug”.— Peston (@itvpeston) September 25, 2019
Watch the full interview at 10.45pm #Peston pic.twitter.com/tL1K12QVm0
Mrs Cox’s widower, Brendan Cox, said this morning that Mr Johnson was “not an evil man” but urged MPs to “take a deep breath”.
He told BBC Radio 4’s Today programme: “I was thinking about how Jo would respond to it last night and I think she would have tried to bring a generosity of spirit to it… and step back from this inferno of rhetoric… what isn’t acceptable is to demonise each other and create this tribal identity.”
He added: “I don’t think he (Johnson) is an evil man… we should remember our humanity… all of us should take a deep breath and step back from this polarisation.”
Commons leader Jacob Rees-Mogg said all people "had a responsibility to be mild in our language when we're speaking in this House or outside”.
"I'm afraid to say it's something where all sides err from time to time and it'd be invidious to pick on individual examples but we have a responsibility of leadership."
Plymouth Tory MP Johnny Mercer said Mr Johnson “should have been more sensitive” but pointed to death threats his family had received.
To be completely clear my kids, wife and I are threatened regularly, BJ should have been more sensitive on Jo, but that aside the outrage is in my view confected from a political class totally devoid of the communities they claim to represent. Dark times. But we will get through. https://t.co/xKeXvAJ8e0— Johnny Mercer MP (@JohnnyMercerUK) September 25, 2019
Mr Johnson’s comments came during a fiery and, at times, bitterly angry session of the Commons where opposition parties again made clear they would not agree to an election until they were sure the threat of a no-deal Brexit on October 31 was off the table.
Downing Street said if opposition MPs did not take up the Prime Minister's offer to table a no-confidence motion, the Government would take it as a mandate to press on with Brexit.