Planned talks this week in Luxembourg are on hold and no additional negotiations are planned.
"Despite intense efforts, some key issues are still open, including the backstop for (Ireland/Northern Ireland) to avoid a hard border", Barnier tweeted after his meeting in Brussels with Raab ended days of bargaining between Barnier's deputy Sabine Weyand and May's Brexit lieutenant Oliver Robbins.
But she said she did not think the two sides were "far apart", adding: "I continue to believe a negotiated deal is the best outcome for the United Kingdom and the EU and that such a deal is achievable, and that is the spirit in which I will continue to work with our European partners".
But after talks which lasted a little over an hour, it was clear that obstacles remained.
"With several big issues still to resolve, including the Northern Ireland backstop, it was jointly agreed that face-to-face talks were necessary ahead of this week's October European Council", said a spokeswoman for Raab's ministry.
The UK can still make progress in Brexit talks despite serious unresolved issues, Downing Street has said.
According to a report from the UK's Observer on Sunday, the DUP has been preparing for a "no deal" Brexit as the most likely outcome, as May's negotiators continued to pursue a deal on the Northern Ireland issue.
Mrs May is now under siege from Tory Eurosceptics and her DUP parliamentary allies and the Government also has a reason to appear to be taking a tough line.
Former Brexit secretary David Davis has urged a Cabinet revolt against the Prime Minister's approach to the talks.
Theresa May has briefed key ministers on the Brexit negotiations amid speculation the Government is moving closer to a deal with Brussels.
The problem of how to prevent the return of a hard border between the British province of Northern Ireland and EU-member Ireland has become the biggest hurdle to a deal on Brexit, Britain's biggest shift in policy for more than 40 years.
The DUP is furious with plans for Northern Ireland to remain fully aligned with rules of the EU's single market after Brexit as this would create new checks on the border between Northern Ireland and the rest of the UK.
The prime minister's counter-proposal is for a temporary customs arrangement for the whole United Kingdom, but Tory Brexiteers fear this becoming an open-ended position that would prevent free trade deals with countries around the world. Whether we do this week or not, who knows?
Britain only wants it in place for a limited time, but Coveney said that "a backstop can not be time limited.
The newspaper said at least nine ministers want Mrs May to change course when the Cabinet meets on Tuesday.
House of Commons leader Andrea Leadsom, International Development Secretary Penny Mordaunt and Work and Pensions Secretary Esther McVey were all poised to quit.
A total of 44 letters demanding a vote were reportedly submitted to the Conservative 1922 Committee - just four short of the number required to trigger a ballot.
Maltese foreign minister Carmelo Abela stressed that all European Union members want to see an agreement to avoid the chaos and economic damage of a "no deal" exit by one of the bloc's biggest economies.
She said the north's citizens will have to pay the price of Brexit, which she described as a "gross act of political and economic vandalism".
Mr Davis is understood to be prepared to run if there is a leadership contest.
Sammy Wilson, the DUP's Brexit spokesperson, said it now believes a no-deal Brexit was nearly inevitable, and described the talks in Brussels as turning into a "battle for the union".
The trouble with the new proposal is that while it would calm the fears of the DUP - which props up May's government - it risks enraging pro-Brexit members of her party who only reluctantly agreed to any kind of transition in the first place.