The PM is in Brussels for a meeting of the European Council, which brings together EU leaders, where she is expected to be told that not enough progress has been made on resolving the Irish border problem.
Former Prime Minister Tony Blair said on Wednesday the government should be ready to ask the European Union for more time to complete divorce talks to avoid the risk of leaving without a deal.
In response to speculation that Mrs May could seek continued membership of the single market for goods, Brexit minister Steve Baker tweeted: "Government policy is, and must remain, to leave the EU's internal market as we leave the European Union".
The British leader is caught between pro-EU parliamentarians who want to retain close economic ties with Britain's biggest trading partner, and pro-Brexit lawmakers who want a clean break so Britain can strike new trade deals around the world.
Irish prime minister Leo Varadkar said he was looking forward to seeing the UK's proposals which will be presented in a white paper.
In its statement, the European Union called for "intensified efforts" to get a deal, and said member states, European Union institutions and businesses should "step up their work on preparedness at all levels and for all outcomes".
He said: "We have made progress but huge and serious divergence remains, in particular on Ireland and Northern Ireland".
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Barnier said he wanted British negotiators to return to Brussels on Monday for renewed talks.
United Kingdom prime minister Theresa May has said that after this date, Britain will no longer be a member of the EU.
The EU27 welcomed progress on the legal text of the withdrawal agreement but noted that "important aspects still need to be agreed" including the territorial application of the deal "notably as regards Gibraltar" - a provision thought to have been inserted at the insistence of Spain.
British Prime Minister Theresa May is to hold a meeting next week with her cabinet to finalize the details of a white paper which will further outline Britain's stance on Brexit.
At the heart of the Brexit impasse is a split within May's Conservative administration about how close a relationship to seek with the European Union after Brexit.
Hounded by divisions within her own cabinet over which path Brexit should take, May has struggled to provide details of her visions for Brexit to the European Union negotiators.
Northern Ireland Secretary Karen Bradley has said the Government's plan will be proposed next month.
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Oil prices have spiked in the past week, and on Thursday crude rose above $74 a barrel for the first time since late 2014. FGE, an energy consultancy, said in its June newsletter that the USA is determined to "push Iran's exports to zero".
As she left the Brussels summit, May said: "We are going to be publishing our White Paper shortly and I want to see the negotiations accelerating and intensifying thereafter".
Britain, meanwhile, is frustrated by what it sees as the bloc's inflexible approach in negotiations.
But Brussels has warned Britain can not maintain the same access to EU-only police databases and institutions.
Britain hopes to get tailor-made arrangements, both on trade and on security.
The UK is running out of time to secure a Brexit deal, European Council president Donald Tusk warned on Friday.
European Commission President Jean-Claude Juncker said the British had to "make clear their position" adding: "We can not go on to live with a split cabinet".
Blair has repeatedly called for reversing Brexit, echoing other critics such as French President Emmanuel Macron and billionaire investor George Soros, who have suggested that Britain could still change its mind.
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