UK Prime Minister Theresa May has said that only a "small number of outstanding issues" stand in the way of a Brexit agreement.
May said the Brexit negotiations are "now in the endgame," adding, "We are working extremely hard, through the night, to make progress on the remaining issues in the Withdrawal Agreement, which are significant."
She also said that she "will not compromise on what people voted for in the referendum. This will not be an agreement at any cost."
May’s comments came as the European Commission warned on Tuesday of "significant" disruption in the UK/EU relationship in the event of a No Deal.
Speaking in Strasbourg, German chancellor Angela Merkel also told MEPs that the UK exit will cause a "deep wound."
Earlier in the day, the UK said there was "optimism on both sides" after negotiations broke up on Monday night.
Both sides want to schedule a special summit of EU leaders at the end of November to sign off on the withdrawal deal, but time is running out.
“This is a very important week for Brexit negotiations. The two negotiating teams have really intensified their engagement” Simon Coveney
Brussels says it will only agree to put the wheels in motion for the summit if an agreement can be reached on the thorny Irish border issue.
If a deal can be reached with the EU in time, May will then need to persuade her party - and the rest of the UK Parliament - to support it in a key Commons vote.
WITHDRAWAL AGREEMENT TEXT ‘ALMOST READY’
The EU’s chief Brexit negotiator Michel Barnier told the EU27 European affairs ministers at the General Affairs Council meeting in Brussels on Monday that the main elements of a UK-EU Withdrawal Agreement text are almost ready and that they will soon be presented to the UK cabinet.
The Irish Foreign Affairs Minister, Simon Coveney, told reporters after the meeting that "this is a very important week for Brexit negotiations," adding, "The two negotiating teams have really intensified their engagement."
Speaking after the meeting with Barnier, Coveney added that the "solidarity from member states for Michel Barnier and his negotiating team is stronger now than it’s ever been."
Meanwhile, the European Commission on Tuesday published detailed information on its ongoing preparedness and contingency work in the event of a no-deal scenario in the Article 50 negotiations with the UK.
The communication outlines a limited number of contingency actions in priority areas that could be implemented if no agreement is reached.
The commission also adopted two legislative proposals to amend existing EU law in the area of visas and energy efficiency to take account of the UK’s withdrawal.
A notice was also published providing extensive information on the changes that will occur - in the event of no deal - for people travelling between the EU and the UK, and vice versa, after 29 March 2019.
It includes information on such issues as border checks and customs controls, driving licenses and pet passports, amongst others.
A commission spokesman said, "While the European Commission is working hard for a deal, and continues to put citizens first in the negotiations, the UK's withdrawal will undoubtedly cause disruption - for example in business supply chains - whether or not there is a deal. Contingency measures cannot remedy the full effects of this disruption."
"In the event of a no-deal scenario, these disruptions will be even more significant, and the speed of preparations would have to increase significantly. Contingency measures in narrowly-defined areas may, exceptionally, be needed in order to protect the interests and the integrity of the EU."
The UK is due to leave the EU next March but the Irish border issue remains the big sticking point to an agreement. The European Parliament also needs to sign off on any agreement and several MEPs have called for an extension to the Brexit talks.