Jeremy Corbyn hijacked an appearance on Facebook by Theresa May to issue a direct challenge to the Prime Minister to take part in a TV debate with him.
But Mrs May dismissed his call, saying that it was more important for her to take questions directly from voters.
Mrs May became the first serving leader of a UK political party to take part in a Facebook Live broadcast, hosted by ITV News as part of the campaign for the June 8 general election, answering questions sent in by users of the social media website.
She discussed her experience of type one diabetes, revealing that she injects herself with insulin four or five times a day, and urged fellow sufferers not to allow the illness to hold them back from doing what they want in life.
And she discussed her taste in fashion, saying that her message to other women wondering what to wear in the workplace was: "Don't be afraid to be yourself."
Presenter Robert Peston then told her he had received a query from "Jeremy Corbyn of Islington", who said: "Hello Theresa May, as Prime Minister you've served your elite friends by giving them tax cuts when wages have stagnated, house-building is at its lowest since the 1920s, there are 20,000 fewer police on our streets since 2010 and the NHS is in crisis.
"Do you not think the British people deserve to see me and you debate live and on television?"
Mrs May responded: "What I think is more important is actually that I and he take questions directly from the voters. I don't think people get much out of seeing politicians having a go at each other, I think people want to hear directly."
ITV will on Thursday host a live televised election debate in Salford, and has said that an invitation to the leaders of the seven biggest parties will remain open until the broadcast starts.
But Mrs May has insisted she will not take part in any televised head-to-head clashes with her rivals, and Mr Corbyn has indicated he will not take part if the Prime Minister is absent.