Boris Johnson has refused to moderate his language during a heated debate in the Commons, despite a barrage of criticism from opposition benches.
Labour's Paula Sherriff referred to Jo Cox, the MP murdered in 2016, as she pleaded with him to refrain from using "dangerous" words like "surrender".
He described her intervention as "humbug" and repeated the word again.
The SNP's Nicola Sturgeon said there was "a gaping moral vacuum where the office of prime minister used to be".
BBC political editor Laura Kuenssberg described scenes in Parliament as an "absolute bear pit".
Mr Johnson was repeatedly challenged over his use of the word "surrender" to describe legislation passed earlier this month which aims to block a no-deal Brexit on 31 October.
Ms Sherriff, the Labour MP for Dewsbury, told the Commons the prime minister had "continually used pejorative language to describe an Act of Parliament passed by this House".
Pointing to a plaque in the chamber, commemorating Mrs Cox, who was murdered by a right-wing extremist, she said: "We should not resort to using offensive, dangerous or inflammatory language for legislation that we do not like, and we stand here under the shield of our departed friend with many of us in this place subject to death threats and abuse every single day."
"They often quote his words 'Surrender Act', 'betrayal', 'traitor' and I for one am sick of it.
"We must moderate our language, and it has to come from the prime minister first."
In response, Mr Johnson said: "I have to say, Mr Speaker, I've never heard such humbug in all my life."
'A threat against my child'
Tracy Brabin, who was elected as MP for Batley and Spen after Ms Cox was murdered, also urged the prime minister to moderate his language "so that we will all feel secure when we're going about our jobs".
Mr Johnson replied that "the best way to honour the memory of Jo Cox and indeed the best way to bring this country together would be, I think, to get Brexit done".
Mrs Cox's husband, Brendan, later tweeted he felt "sick at Jo's name being used in this way".
The best way to honour her is to "stand up for what we believe in, passionately and with determination", he tweeted.
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
Liberal Democrat leader Jo Swinson said the prime minister was an "utter disgrace" for his response to the questions on his language.
She told MPs: "I today have reported to the police a threat against my child. That has been dismissed as 'humbug'.
"This is a disgraceful state of affairs and we must be able to find a way to conduct ourselves better."
Leader of the Independent Group for Change, Anna Soubry, said it "takes a lot to reduce this honourable member to tears" but she said she is "not alone tonight".
"There are others I believe who have left the estate, such has been the distress," she told MPs.
"In this, the most peculiar and extraordinary of political times, the language that is used is incredibly important.
"We have evidence, whatever side of the debate you are on, when you use word like 'surrender', 'capitulation', and others use the word 'traitor' and 'treason', there is a direct consequence.
"It means my mother receives a threat to her safety. It means my partner receives a death threat."
Labour leader Jeremy Corbyn urged the Speaker to unite the party leaders "to issue a joint declaration opposing any form of abusive language or threats and to put this message out to our entire community that we have to treat each other with respect".
Speaker John Bercow said he was "very open to convening a meeting of senior colleagues for the purpose of a House-wide public statement".
Conservative MP Stephen Crabb told BBC Newsnight that he was "shocked by the way [the PM] responded to the remarks about Jo Cox".
He said Mr Johnson had "strong support among Conservative MPs... but he also has a duty as prime minister to try to bring unity to our country and reduce the level of poison in our politics".
Culture Secretary Nicky Morgan said the prime minister was "aware and sympathetic" to the threats MPs have received.
"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.
I know the PM is aware of & sympathetic about the threats far too many of us have received because I shared with him recently the threats I am getting. But at a time of strong feelings we all need to remind ourselves of the effect of everything we say on those watching us.— Nicky Morgan MP (@NickyMorgan01) September 25, 2019