"President Juncker underlined that the EU27 will not reopen the Withdrawal Agreement, which represents a carefully balanced compromise between the European Union and the UK, in which both sides have made significant concessions to arrive at a deal", the statement said.
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Juncker, at the same time, expressed willingness to amend the political declaration agreed by London and Brussels in order to be more ambitious in terms of the content of the future EU-UK relationship.
"The Prime Minister and the President will meet again before the end of February to take stock of these discussions", the statement read further.
At the same time, May said she would try to seek alternative arrangements on the issue, following the vote of the House of Commons, urging the government to replace the Irish backstop deal with another kind of agreement.