Mr Khan said he was “really sorry” for saying in relation to London Assembly member Peter Fortune: “For somebody who reads a lot, he ain’t half thick.”
Mr Khan paused during a session of mayor’s question time at City Hall on Thursday morning to tell members: “Can I just apologise unreservedly to Peter Fortune for calling him thick.
“I am really sorry for saying that. I have reflected on that and I shouldn’t have said that. It’s not appropriate for me to have said that, and I’m really sorry – genuinely.”
The mayor then went over to Mr Fortune during a break in proceedings and, holding his hands up, repeated the apology face to face.
Mr Fortune told the Standard that he accepted Mr Khan’s apology but said the mayor too often resorted to “playground insults” in an apparent bid to avoid answering questions.
The pair had clashed earlier in Thursday’s session over the ability of the Ulez to reduce pollution and improve child health.
In the exchange, Mr Fortune said to the mayor: “You can be a little bit slippy.”
This prompted Andrew Boff, the chairman of the London Assembly, to warn: “We should not be using personal abuse in this chamber. It’s not helpful. It makes us look a bit seedy.”
Mr Fortune, who is renowned for his forensic style of questioning, had been seeking to interrogate Mr Khan about the actions of his deputy mayor for the environment, Shirley Rodrigues.
Mr Fortune claimed there was email evidence of Ms Rodrigues “leaning on experts” to get them to comment on the Ulez or its predecessor, the low emission zone, in a way that was “beneficial” to the mayor.
Mr Khan said: “I have read the entire email chain. I think there is nothing wrong in Shirley Rodrigues talking to experts in the way that she did.”
Mr Khan is facing an investigation by the City Hall watchdog for misleading the assembly in relation to what he knew about the consultation into expanding the Ulez London-wide.
The investigation is also considering remarks made by Mr Khan at a public meeting in Ealing, in which he said anti-Ulez campaigners were “joining hands” with the far-Right.
Mr Khan and Tory assembly members often exchange insults during Mayor’s question time but it is rare for Mr Khan to make such a fulsome apology in public.
Mr Fortune said: “Being mayor of the city we all call home is a huge job, there’s no denying it.
“I accept the mayor’s apology, but that job comes with responsibility, not only to accept and respond openly to scrutiny, but also to set a better example of behaviour in public life.
“When his deputy mayor has been caught trying to manipulate data to back his policies, and he himself is under investigation for his own use of language, it’s right we ask hard-hitting questions.
“Londoners need a mayor that tackles scrutiny head on, not like Sadiq Khan - who would rather skirt the question, and resort time and time again to playground insults.”