Here is Prime Minister Theresa May's speech in full:
"Yesterday, I was in Salzburg for talks with European leaders.
"I have always said that these negotiations would be tough - and they were always bound to be toughest in the final straight.
"While both sides want a deal, we have to face up to the fact that - despite the progress we have made - there are two big issues where we remain a long way apart.
"The first is our economic relationship after we have left.
"Here, the EU is still only offering us two options.
"The first option would involve the UK staying in the European Economic Area and a customs union with the EU.
"In plain English, this would mean we'd still have to abide by all the EU rules, uncontrolled immigration from the EU would continue and we couldn't do the trade deals we want with other countries.
"That would make a mockery of the referendum we had two years ago.
"The second option would be a basic free trade agreement for Great Britain that would introduce checks at the Great Britain/EU border. But even worse, Northern Ireland would effectively remain in the Customs Union and parts of the Single Market, permanently separated economically from the rest of the UK by a border down the Irish Sea.
"Parliament has already - unanimously - rejected this idea.
"Creating any form of customs border between Northern Ireland and the rest of the UK would not respect that Northern Ireland is an integral part of the United Kingdom, in line with the principle of consent, as set out clearly in the Belfast/Good Friday Agreement.
"It is something I will never agree to - indeed, in my judgement it is something no British Prime Minister would ever agree to. If the EU believe I will, they are making a fundamental mistake.
"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.
"But I have also been clear that the best outcome is for the UK to leave with a deal. That is why, following months of intensive work and detailed discussions, we proposed a third option for our future economic relationship, based on the frictionless trade in goods. That is the best way to protect jobs here and in the EU and to avoid a hard border between Ireland and Northern Ireland, while respecting the referendum result and the integrity of the United Kingdom.
"Yesterday Donald Tusk said our proposals would undermine the single market. He didn't explain how in any detail or make any counter-proposal. So we are at an impasse.
"The second issue is connected to the first. We both agree that the Withdrawal Agreement needs to include a backstop to ensure that if there's a delay in implementing our new relationship, there still won't be a hard border between Ireland and Northern Ireland.
"But the EU is proposing to achieve this by effectively keeping Northern Ireland in the Customs Union.
"As I have already said, that is unacceptable. We will never agree to it. It would mean breaking up our country.
"We will set out our alternative that preserves the integrity of the UK. And it will be in line with the commitments we made back in December - including the commitment that no new regulatory barriers should be created between Northern Ireland and the rest of the UK unless the Northern Ireland Executive and Assembly agree.
"As I told EU leaders, neither side should demand the unacceptable of the other.
"We cannot accept anything that threatens the integrity of our union, just as they cannot accept anything that threatens the integrity of theirs.
"We cannot accept anything that does not respect the result of the referendum, just as they cannot accept anything that is not in the interest of their citizens.
"Throughout this process, I have treated the EU with nothing but respect. The UK expects the same. A good relationship at the end of this process depends on it.
"At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and counter proposals.
"So we now need to hear from the EU what the real issues are and what their alternative is so that we can discuss them. Until we do, we cannot make progress.
"In the meantime, we must and will continue the work of preparing ourselves for no deal.
"In particular, I want to clarify our approach to two issues.
"First, there are over 3 million EU citizens living in the UK who will be understandably worried about what the outcome of yesterday's summit means for their future.
"I want to be clear with you that even in the event of no deal your rights will be protected. You are our friends, our neighbours, our colleagues. We want you to stay.
"Second, I want to reassure the people of Northern Ireland that in the event of no deal we will do everything in our power to prevent a return to a hard border.
"Let me also say this.
"The referendum was the largest democratic exercise this country has ever undergone. To deny its legitimacy or frustrate its result threatens public trust in our democracy.
"That is why for over two years I have worked day and night to deliver a deal that sees the UK leave the EU.
"I have worked to bring people with me even when that has not always seemed possible.
"No one wants a good deal more than me.
"But the EU should be clear: I will not overturn the result of the referendum. Nor will I break up my country.
"We need serious engagement on resolving the two big problems in the negotiations. We stand ready."