"I will be armed with a fresh mandate, new ideas and a renewed determination to agree a pragmatic solution that delivers the Brexit the British people voted for, while ensuring there is no hard border between Northern Ireland and the Republic of Ireland", said May.
After the Commons voted on the Brady amendment, the EU's chief negotiator Michael Narnier said the backstop is "part and parcel" of the UK's Brexit deal and will not be renegotiated. Sign-up now and enjoy one (1) week free access!
May said she is going back to Brussels to battle for Britain and Northern Ireland.
"I'm determined to deliver Brexit, and determined to deliver on time - on March 29, 2019", she wrote.
May said she is determined to deliver Brexit on time.
UK MPs last week backed a call for May to return to Brussels to secure a new Brexit deal that puts "alternative arrangements" in place of the controversial backstop - a kind of insurance policy created to avoid a hard border between Northern Ireland and the Irish Republic.
In another development, the European Commission has agreed to compensate Irish farmers for a collapse in market value in the event of a no-deal Brexit, the Irish edition of the Sunday Times newspaper said, quoting Irish government and EU sources.
But Maas rejected British calls for further concessions to be offered to make the deal, negotiated over two years, more palatable to its critics in London.
Foreign Secretary Jeremy Hunt conceded on Thursday that "extra time" might be needed to get "critical legislation" related to Brexit through Parliament.
May is scheduled to report back to the Commons regarding the results of her discussions with the European Union on the 13th of February, with the MPs expected to vote the next day.
Under the terms of the deal, the United Kingdom would remain in the customs union until an alternative arrangement is found that ensured the avoidance of a hard border.
He added that Britain's only path to avoiding a so-called "hard Brexit", in which London exited automatically on March 29 with no transitional arrangements in place to ensure the continued flow of goods, medicines and transport links, was to accept the existing deal.
Baker will be among Conservatives meeting with Brexit minister Stephen Barclay on Monday, May's office said, to discuss a compromise plan put forward by a group of lawmakers to find an alternative to the backstop.
May is due to report back to parliament on her negotiations with the European Union on 13 February, a few weeks after she secured MPs' support to go back to Brussels.