He has also denied threatening MPs who have opposed him with mass sackings before the next general election.
This morning Conor McGinn, the Labour MP for St Helens, wrote about how Corbyn had said he would ring his father - a Sinn Féin councillor - after McGinn had urged him to broaden his appeal in an interview in May.
'The leader of the Labour Party was proposing to address an issue with one of his own MPs by ringing his Dad.
Mr McGinn said Mr Corbyn had initially asked for his resignation and considered sacking him after the comments in The House magazine but subsequently reconsidered.
But subsequently, through his spokesman, he had asked for an apology and retraction, which Mr McGinn refused to do.
In a statement, Mr McGinn said he and other Labour MPs had been subjected to a "torrent of abuse and threats" from supporters of Mr Corbyn.
Labour MPs would have to put themselves up for reselection after electoral boundaries are redrawn in 2018, Jeremy Corbyn said as he launched his campaign to remain as party leader.
'Thankfully others dissuaded Jeremy from taking this course of action. He said: "This is untrue".
"It is not good enough for Jeremy to say he has threats too".
However, Owen Smith, who is challenging Corbyn for the leadership of the party, said he believed McGinn's account.
Mr Smith told Sky News he had received death threats and the problem of abuse had not been there before Mr Corbyn's leadership win. "I don't do any abuse, I don't do any bullying".
He told Sky News: "I wish some of my colleagues would concentrate on political issues". And I hope that those that may not agree with me politically, may not even like me personally - I hold out the hand of friendship to them all, because come September when this election is done and dusted, there will still be a Tory government in office, there will still be grotesque levels of inequality in our society, there will still be whole parts of this country that are left-behind Britain.
"I don't think he feels he can bring the party back together, that's why he's talking about re-selections because I think he is reconciled". We've done that spectacularly.
"We are now the largest membership we have ever had. We need to listen and develop policies that are relevant today and fix the damage and hurt suffered by so many people, and go on to build a nation that proves it truly cares about people by the good quality of life experienced by all".
The latest row blew up at a time when Angela Eagle has been advised by police not to hold public meetings in her Wallasey constituency.
Corbyn, who launched his leadership campaign earlier on Thursday, also said securing access to European markets would be a key party of any Brexit deal, but he also wanted to see some freedom of movement retained.
In a separate interview with the BBC, Mr Corbyn attacked her for the suggestion that he had "stirred" abuse.
Conventional wisdom has it that the beneficiary will again be Mr Corbyn who was propelled to an overwhelming victory in last year's contest with the support of the £3 members.