The spokesman said the government's motion that will be debated and voted on would be published later on Monday.
The plans include the UK Government's approach to tariff rates for imports and the Irish border if it leaves without a deal.
"The PM and negotiating teams are focused on making progress so we can secure parliament's support for the deal".
But MPs rejected it in January by a massive 432 votes to 202, with many of May s Conservatives rebelling against her.
In remarks released late Tuesday, Maas said the U.K. Parliament's decision to reject the deal "brings a no-deal scenario ever closer".
The MLA for Foyle commented: "Sooner or later, the British Parliament is going to have to support a Backstop for Northern Ireland or else support no Brexit at all; there is no happy medium between these two eventualities".
The EU warned British politicians that negotiations will not be reopened if Parliament rejects the deal again.
In a written legal opinion, Cox said that if U.K. -EU negotiations became stalled through "intractable differences", Britain would have "no internationally lawful means of exiting the Protocol's arrangements, save by agreement". May flew to Strasbourg, France, to seek revisions, guarantees or other changes from European Commission president Jean-Claude Juncker that would persuade reluctant British legislators to back her withdrawal agreement with the EU, which they resoundingly rejected in January.
Three new papers will be presented to Parliament on Tuesday: "this joint legally binding instrument on the withdrawal agreement which also commits the European Union and United Kingdom to find alternative arrangements to replace the backstop by December 2020 and a joint statement to accompany the political declaration which outlines a number of commitments to expedite the process of bringing into force the future agreement".
On the Irish border, the British government said it would not introduce any new checks or controls on goods moving from the Irish Republic to the British province of Northern Ireland in the event of a no-deal Brexit, stressing the plan was temporary and unilateral.
"Let's be crystal clear about the choice: it is this deal or Brexit might not happen at all", he said.
Just 18 days before the United Kingdom is due to leave the European Union, there is still no ratified divorce deal and talks with the bloc stalled over the weekend as May felt she was unable to break the political deadlock in London.
Wilson said the DUP chose to vote against May's deal as soon as they read the legal advice by Britain's attorney general, which, he said, showed nothing had changed after Monday's revisions to the deal.
MPs could get the chance to extend Brexit this week if Theresa May's deal to leave the European Union is once again rejected by the Commons and MPs vote to take no-deal off the table.
"If this deal is not passed then Brexit could be lost", May said, her voice ragged after days of frantic shuttle diplomacy.
May offered lawmakers the vote on Tuesday on what she had hoped would be a revised deal.
The Daily Mirror instead described the Prime Minister's trip to Brussels on Monday night as a desperate and "theatrical" bid to convince her MPs to back her "bad deal".
"We're very clear that the Withdrawal Agreement can't change but we want to try to be helpful in terms of providing the clarity and reassurance that's needed in Westminster that the backstop is meant to be temporary", Ireland's Coveney said.