Radio presenter John Humphrys’ controversial off-air comments about the equal pay row at the BBC, which he has defended as “jokey”, can be heard in a leaked recording.

The broadcasting veteran is heard to say he could hand over more than the entire salary of his colleague North America editor Jon Sopel, and still be “left with more than anybody else”.

The recording of a conversation between Humphrys and Sopel, before Monday’s BBC Radio 4 Today programme, heard them discussing Carrie Gracie who had announced just hours earlier that she had quit as the BBC’s China editor in protest at unequal pay.

In a BBC pay disclosure last year Humphrys was listed as having a salary of between £600,000 and £649,999, making him the BBC’s highest-paid news presenter.

North America editor Jon Sopel was listed as having a salary of between £200,000 and £249,999, while Gracie revealed she had been earning £135,000 before the BBC offered her a £45,000 rise, which she rejected.

Gracie’s resignation came as she accused the corporation of a “secretive and illegal pay culture” and called for men and women at the corporation to be paid the same.

In the conversation, a recording of which has been obtained by Buzzfeed News, Mr Humphrys asked his colleague how much of his salary he would be prepared to “hand over” to keep Ms Gracie.

He is heard saying: “And I could save you the trouble because I could volunteer that I’ve handed over already more than you f****** earn, but I’m still left with more than anybody else, and that seems to me to be entirely just. Something like that would do it, do you think?”

He adds: “Dear God. She’s actually suggested that you should lose money. You know that, don’t you? You’ve read the thing properly, have you?”

In an open letter, Gracie said she had left her post to “speak out publicly on a crisis of trust at the BBC”, adding she simply wanted the corporation to “abide by the law and value men and women equally”.

Mr Humphrys told ITV News he backed equal pay, stating: “We are in habit, Jon and I, of winding each other up and the purpose of this jokey – I emphasise jokey – exchange was a bit of mutual mickey-taking, and that is all it was.

“It was not meant for any other ears than Jon’s, although there happened to be a producer in the studio at the time, a woman as it happens, who thought it was very funny.

“I had no idea, neither did John, neither did anybody else, including the producer, that it was being recorded somewhere in the bowels of the BBC and somebody chose to leak it. And that, er, yeah, was mildly annoying.

“I was being sarcastic. It was a joke on me, rather than a joke on Jon. It was a jocular exchange. It did not represent my views – exactly the opposite. It was meant to be a bit satirical, ‘yeah well, you, Sopel, you’re not worth tuppence’, you know, it was that sort of exchange.

“And if people took it – took a different message from it, it could only be because they didn’t appreciate that it was a joke. But then they weren’t ever meant to hear it, do you see?”

A BBC spokeswoman said of the controversy: “This was an ill-advised off-air conversation which the presenter regrets. The BBC is committed to getting its pay structures right and, as we have said, we are conducting a comprehensive analysis of presenter pay.”

A Downing Street spokesman said: “I think the Prime Minister is very clear that tackling injustices like the gender pay gap is part of building a country that works for everyone and she has said she wants to see women paid equally with men and it’s important the BBC continues to take this seriously and carries on publishing figures in the future so we can see the progress they are making.”