Jeremy Corbyn posed his own question to Theresa May during her Facebook Live appearance on ITV News.
The Labour leader issued Mrs May a direct challenge to take part in a TV debate with him, but the prime minister rejected the idea, saying she would rather take questions directly from voters.
Mrs May became the first serving leader of a UK political party to take part in a Facebook Live event as she took questions from the public, put to her by ITV News Political Editor Robert Peston.
During the session, Peston told told the prime minister 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 replied: "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."
Mr Corbyn later responded on Twitter: "Thanks Peston for reading my question to Theresa May asking why she won't debate me. It's weak leadership to hide from your record."
On Thursday, ITV will host a live televised election debate, with the leaders of the seven biggest parties all invited to take part.
However, 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.