Jeremy Corbyn has refused to suspend a Labour MP who referred to a Conservative London Assembly Member as a "token ghetto boy".
Kensington MP Emma Dent Coad apologised for a 2010 blog post about Shaun Bailey, which he branded a "hate-filled, racist article" after it emerged earlier this week.
But Mr Bailey dismissed the form of Ms Dent Coad's apology as a "cowardly response" and had written to Mr Corbyn demanding "the strongest disciplinary action possible".
He was supported by Tory MPs James Cleverly and Kemi Badenoch, who also sent a letter to the Labour leader asking whether he will condemn Ms Dent Coad and suspend her pending an investigation.
But, commenting on the row for the first time, Mr Corbyn insisted he is "not going to withdraw the whip" from Ms Dent Coad, who was elected to Parliament in June.
"I will obviously ensure people discuss the use of language with people," the Labour leader added.
"I will make sure everyone treats others with respect."
In the blog post, Ms Dent Coad claimed Mr Bailey - who was standing as a Conservative parliamentary candidate in Hammersmith at the time - had stigmatised the area by referring to it as a "ghetto".
She wrote: "Who can say where this man will ever fit in, however hard he tries? One day he is the 'token ghetto boy' standing behind D Cameron, the next 'looking interested' beside G Osborne. Ever felt used?"
On Tuesday, Ms Dent Coad offered an apology to Mr Bailey, telling the BBC: "If he was offended by me repeating what other people have said then I do apologise.
"Clearly, I shouldn't have repeated it. People have taken it the wrong way."
But, criticising Ms Dent Coad's response, Mr Bailey accused her of attempting to "blur and camouflage the views she expressed in her blog by falsely dressing them up as someone else's words".
He added: "Despite her claims, she can provide no evidence that I or anyone else used the horrendous terms she advocated."
The Guido Fawkes website has since published a further 2010 blogpost from Ms Dent Coad, in which a stick figure being hanged features alongside the caption "new logo needed for Tories".
In their letter to Mr Corbyn, Mr Cleverly and Mrs Badenoch also called on Mr Corbyn to address Labour's "condescending attitude to BAME voters and candidates".
They highlighted a Twitter post by Labour MP Clive Lewis, in which he told a fellow user: "If you think you can fight racism and be in the Tory party then I guess this conversation isn't going to go very far."
The pair also referred to Mr Corbyn's claim during June's General Election campaign that "only Labour can be trusted to unlock the talent of Black, Asian and Minority Ethnic people."
Ms Dent Coad previously sparked controversy with her comments about the Royal Family during the Labour party conference in September.