(Photo: CGTN)

"No deal is better than a bad deal" and a Brexit deal must include an Irish backstop, British Prime Minister Theresa May said on Friday in a statement given inside her Downing Street office.

May made the remarks a day after European Union (EU) leaders rejected key parts of her Brexit deal proposals during an informal summit in Salzburg, Austria.

In her speech on Friday, May said the EU must come up with an alternative to her Brexit proposals, saying talks had reached an impasse after the rejection by the bloc.

"It is not acceptable to simply reject the other side's proposals without decent explanation and counter proposal," she added.

During the summit, EU leaders warned May that unless she gave ground on trade and the Irish border by November, they are willing to let Britain leave the trading bloc without any kind of deal.

Addressing that particular request, May said she could not agree to any deal which treated Northern Ireland (NI) differently to the rest of the United Kingdom.

"Anything which fails to respect the referendum or which effectively divides our country in two would be a bad deal and I have always said no deal is better than a bad deal," May stressed. 

Earlier, her Brexit Secretary Dominic Raab said some EU leaders had shown unstatesmanlike behavior in Salzburg.

"We've already compromised hugely with the Chequers proposals. We've engaged and we want to hear more about what the real critique of it is and we've got no other credible alternatives on the table," Raab told the BBC.

"What we're not going to do is be salami sliced throughout this negotiation in a typical style that the EU engages in without movement on the other side."