Zac Goldsmith has accused Sadiq Khan of "playing the race card" in the contest to succeed Boris Johnson as London mayor.
Goldsmith has accused his Labour rival of having "divisive and radical politics". Khan hit back, warning Goldsmith the attack would be seen as a coded attack on his Muslim faith.
Defending his comments, Goldsmith told BBC Radio 4's Today programme he was referring to the leftwing trajectory of the Labour Party and was not trying to link Khan to extremism.
"I think whats happened to the Labour Party in the last few months is more radical than anything I have seen in my lifetime," he said.
But Today presenter Sarah Montague asked: "We are in world where there is a huge amount of coverage of the concerns of Islamist terrorism and you are calling the Muslim candidate, your rival, 'radical and divisive', do you think that is wise?"
Goldsmith said the selection of Jeremy Corbyn and Khan by Labour members showed the party was now "extreme" and that the "same people" who chose Corbyn had chosen Khan.
He said: "If I can not use the term 'radical' to describe what has happened to the Labour Party the selection of these two candidates if i cant use the terms radical in that context then I don't know..."
"I think he is playing with fire. I don't think there is anything more divisive than playing the race card when clearly, unambiguously, it does not apply.
"It's very obvious that what I was referring to when I described him as a radical candidate as part of a radical process that has enveloped the Labour Party and taken our politics in an extraordinary direction."
In an interview with The Sunday Times, Khan warned Goldsmith his language would be seen as targeting his faith. "Calling someone divisive and radical, be very careful how that’s perceived," he said.
"You’re playing with fire. When you say that about a candidate of Islamic faith, what are you implying? That will come back and bite you in the bum if you resort to that."