German Foreign Minister Heiko Maas tells the Funke newspaper group published Sunday that "we need clear proposals from London" and rejected a suggestion that the EU's position is increasing the risk of a no-deal Brexit. The Irish border issue has proven to be a major stumbling block in ongoing UK-EU Brexit negotiations.
But prominent eurosceptic Conservative Steve Baker said many pro-Brexit lawmakers had broader concerns about her deal.
"When I return to Brussels I will be battling for Britain and Northern Ireland, I will be armed with a fresh mandate, new ideas and a renewed determination to agree a pragmatic solution".
Writing in the Sunday Telegraph, May suggested that Labour leader Jeremy Corbyn had agreed with her that the Irish border backstop as set out in the Withdrawal Agreement had to change.
He is the second senior minister to suggest such a delay may be needed, after Foreign Secretary Jeremy Hunt said on Thursday Britain may need time to get legislation through.
The Prime Minister is due to report back to Parliament on her negotiations with the European Union on February 13, with a further series of votes by MPs expected the following day.
Last week Mrs May secured Parliament's backing to go back to Brussels in the hope of hammering out a fresh agreement that does not include the Irish border backstop - which is unacceptable to the DUP and Brexiteer Tories - and which will command a majority in the Commons.
Police are continuing to investigate Friday's discovery of a cache of ammunition in the Omeath area on the Cooley Peninsula near the border with Northern Ireland.
This would probably mean checks on goods crossing it, unless both sides could reach a comprehensive trade deal.
A number of MPs fear the United Kingdom could be "trapped" in this arrangement for years, leaving it unable to strike its own trade deals on goods with the rest of the world.
Our political correspondent Chris Mason said that while Mrs May pledged to "go back to Brussels to secure a plan that Parliament can stand behind", the European Union remains publicly opposed to changing the backstop.
Mrs. May wrote: "While replacing the backstop with alternative arrangements was one option, [Sir Graham] would also be happy with the current backstop if there was a time limit or unilateral exit mechanism".
The Irish backstop has been proven to be the primary sticking point in the Brexit talks. "By a majority of 16, MPs said that, with changes to the Northern Ireland backstop, they would support the deal that I agreed with Brussels to take us out of the European Union".