The Prime Minister said the Labour leader had “opposed every move” by the Government to get a deal, adding that he was a “fine one to talk” about uniting the nation given his initial refusal to meet her in Downing Street for talks.
Mr Corbyn warned that Mrs May had “got to move on from the red lines she put down in the first place” and reiterated his belief that a customs union and “strongest possible deal” with the single market will break the Brexit impasse.
He added that the PM also may have temporarily united her “very divided party” but must make compromises to secure jobs and living standards in the UK.
Their exchanges at Prime Minister’s Questions came ahead of a meeting in Downing Street, and after MPs backed amendments to reject a no-deal Brexit while also seeking changes to the controversial Northern Ireland backstop proposal in the Withdrawal Agreement.
Speaking in the Commons, Mr Corbyn asked the PM to outline the “alternative arrangements” to the backstop.
Mrs May said there were a number of options, adding: “Last night the House voted to set a clear direction on the way the House could agree a deal and that is about dealing with the issue of the backstop.
“I say again, there are a number of proposals for how that could be done.
“They (Conservative MPs) have put forward proposals such as a unilateral exit mechanism or a time limit to the backstop, and the Political Declaration already references alternative arrangements and raises a number of proposals that could be addressed such as mutual recognition of trusted trader schemes.”
Mrs May, in response to a further question, added: “(Mr Corbyn) stands up regularly and says he doesn’t want no-deal. I’m working to ensure we get a deal.
“He has opposed every move by this Government to get a deal. He’s the one who is risking no-deal.”
Mr Corbyn reiterated that MPs had voted to remove a no-deal Brexit before telling Mrs May: “I look forward to meeting the Prime Minister to discuss a solution that could, in my view, unite the country. Changes to the backstop alone will not be sufficient.”
He added: “The Prime Minister may have succeeded in temporarily uniting her very divided party but is she willing to make the compromises necessary that are more important - and that is to unite the country going forward to secure jobs and living standards right across the UK.”
Mrs May replied to the Labour leader: “He’s a fine one to talk about coming together when it was only last night that he agreed to actually meet me to talk about these issues.
“Time and time again he has told me to listen to the views of the House. He’s just stood up and said the backstop is not the only issue in the Withdrawal Agreement.
“Last night the House voted by a majority to say the issue that needed to be addressed was the backstop.
“So, he needs to listen to the House and to recognise that.”
Mrs May said Mr Corbyn’s customs union and single market proposal was rejected by MPs on Tuesday.