Ms Dugdale said she “utterly refuted” suggestions that Mr Khan had compared nationalism in Scotland with racism as he addressed the party’s conference at the weekend.
The row overshadowed much of the Spring gathering in Perth as Nicola Sturgeon slammed to the comparisons.
Mr Khan said during the conference speech on Saturday that there is “no difference between Scottish nationalism and racism.”
He appeared to subsequently win support from Scottish labour health spokesman Anas Sarwar, who said: “All forms of nationalism rely on creating us and them - let’s call it for what it is.”
But Ms Dugdale insisted that the London mayor had not branded the SNP as racist.
“I utterly refute that that is what Sadiq Khan said and I have never suggested and never would suggest that the SNP are an inherently racist party,” she told the BBC’s Sunday Politics.
“That does our politics a dis-service and it brings out the worst.”.
She added: “Our politics in Scotland is divided enough. I do not want to revisit that independence question again for exactly that reason and many others.
“What I want to do as leader of the Labour party is try and bring our country back together, appeal to people who voted both Yes and No.”
As Mr Khan addressed party activists he insisted: “There’s no difference between those who try to divide us on the basis of
whether we’re English or Scottish, and those who try to divide us on the basis of our background, race or religion.”
He went on to clarify that was was “not saying that Nationalists are bigots or racists.”
But the comments came under fire from Nicola Sturgeon who said it showed Labour is “in a hole.”
The First Minister added: “It’s desperation. We should rise above it.”
But Ms Dugdale sought to downplay the remarks yesterday.
“I think Sadiq Khan was very clear that he wasn’t accusing the SNP of racism - what he was saying very clearly though is
that nationalism by its very nature divides people, divides communities.
“That’s what I had said in my speech yesterday - I said we’re living in a divided and fractured country, a divided and fractured society. Politics is forcing us constantly to pick sides - whether you are Yes or No, Leave or remain.
“It brings out the worst in our politics, the worst in our politicians and all the consensus, the progress that we normally find
in the grey areas is lost.
“That’s why I’m standing at this conference under a banner that `Together we’re Stronger.’
“But we have to come up with ideas and values and principles that can bring communities back together, very firmly focussed
on the future. That’s where I agree with Sadiq Khan.