“We will not accept any going back on this joint report. This progress has been agreed and will be rapidly translated into a withdrawal accord that is legally binding in all three areas and on some others that remain to be negotiated,” Barnier told EU lawmakers on Wednesday.
Barnier added that the complex negotiations have progressed, but further steps are required to secure the UK’s orderly withdrawal from the EU.
"We are not at the end of the road, neither regarding citizens' rights nor for the other subjects of the orderly withdrawal. We remain vigilant," he noted.
His remarks came after his British counterpart David Davis undermined the agreement reached last Friday, saying it was “a statement of intent” rather than being legally binding.
Meanwhile, British Prime Minister Theresa May has asked lawmakers to vote on the final Brexit deal before the EU parliament takes its decision on the issue.
"We will put the final withdrawal agreement between the UK and the EU to a vote in both houses of parliament before it comes into force," May told parliament on Wednesday.
The British premier made the comments, as lawmakers assembled to discuss her administration’s bill which aims to copy the existing EU law into the domestic ones.
"We expect the UK parliament to vote ahead of the European parliament so we fully expect parliament to vote well before March 2019," she added.
May also warned that the amendment to the draft deal made by the Conservative party could endanger Brexit’s order. She said the amendment at this stage of the talks could hamper Britain’s smooth exit from the EU.
"Of course after we leave, the withdrawal agreement will be followed up by one or more agreements covering different aspects of the future relationship and we will introduce further legislation where it is needed to implement this into UK law, providing yet another opportunity for proper parliamentary scrutiny," she said.
The EU-UK agreement paves the way for the beginning of the second phase of negotiations that deal with financial and security matters.
An EU summit starting Thursday must approve the Brexit agreement for the negotiations to move on to the next phase, and the parliament also has to back the overall agreement for Britain to leave the EU on March 29, 2019.