The deal struck between EU President Jean Claude Juncker and Theresa May does not undermine the Withdrawal Agreement, Government sources said.
The British Government insisted it had secured legally binding changes to the deal, whereas the EU and the Irish Government all that was agreed were legally binding assurances, which complement rather than undercut the Withdrawal Agreement.
“It is a unilateral statement from the UK, Ireland is comfortable with that. It is in addition to the Withdrawal Agreement,” a government source said.
In a letter addressed to European Council president Donald Tusk, Mr Juncker said that "our hand must remain outstretched" to the UK and that "we should continue to support the efforts of Prime Minister May to ensure an orderly withdrawal".
"While fully respecting the principles defined unanimously by the European Council we should - following the request of Prime Minister May - now give one last push to get the Withdrawal Agreement over the finishing line," said Mr Juncker in the letter.
He sent Mr Tusk the text of an instrument relating to the Withdrawal Agreement and a joint statement supplementing the Political Declaration, agreed between him and Mrs May and endorsed by the European Commission.
He said that Irish Taoiseach Leo Varadkar had informed him that he "would be prepared to accept this solution in the interest of securing an overall deal".
Mr Juncker recommended that the leaders of the 27 remaining EU states give their endorsement to the documents at the European Council summit of March 21-22 in Brussels, subject to them having been approved by that time by the House of Commons.
"I believe it is high time to complete the withdrawal process in line with the wishes expressed by the Government of the UK and to move on as swiftly as possible to the negotiation of our future partnership," wrote Mr Juncker.
The Commission is ready to start talks on the future partnership "immediately after the Withdrawal Agreement is signed", he said.
Mr Juncker said that the UK's withdrawal should be complete by the time of the European Parliament elections of May 23-26.
If it was not complete, the UK would be legally required to take part in the elections, he said.
The British Government released the text of the motion for Tuesday's Commons vote, which asks MPs to approve five documents - the Withdrawal Agreement (WA) and Political Declaration agreed in November along with three others finalised in Strasbourg on Monday.
The motion defines the first new document as "the legally binding joint instrument" relating to the WA "which reduces the risk that the UK could be deliberately held in the Northern Ireland backstop indefinitely and commits the UK and EU to work to replace the backstop with alternative arrangements by December 2020".
The second new document is described as a "unilateral declaration by the UK" which sets out "the sovereign action the UK would take to provide assurance that the backstop would only be applied temporarily".
The final document is a supplement to the Political Declaration "setting out commitments by the UK and the EU to expedite the negotiation and bringing into force of their future relationship".
Government ministers will be hauled back into a late night emergency cabinet meeting after 10.30pm tonight due to fears Britain could undermine two years of Brexit talks by seeking a "unilateral" right to walk away from the backstop.
Sources told the Irish Examiner the late night discussions will take place in Dublin city centre just after 10.30pm tonight after a two-hour emergency cabinet meeting was earlier adjourned.
Despite holding an earlier scheduled general cabinet meeting this morning, ministers who were preparing to travel across the globe for the St Patrick's day festivities were ordered back to Government Buildings for an emergency cabinet meeting at 6.45pm.
This was because of major developments on Brexit, with British prime minister Theresa May and European Commission president Jean Claude Juncker preparing to meet for last ditch talks in Strasbourg.
It is understood these talks centred on three points:
Taoiseach Leo Varadkar gave an update on developments in the preceding hours when the emergency cabinet meeting began at 6.45pm.
After discussions described as "full and frank, with lots of interaction" from ministers, he then adjourned cabinet at 7.45pm to take a phone call from European Commission president Jean Claude Juncker.
During this phone call Mr Juncker updated Mr Varadkar on his initial discussions with British prime minister Theresa May.
The Taoiseach returned to inform ministers of the updated situation, saying there are no concerns about the withdrawal agreement changing or an agreed joint statement on how to interpret the backstop.
However, he said Britain wants to be able to publish a "unilateral" declaration on their view of the backstop which the Government has yet to see - an issue that could cause serious problems for Ireland's Brexit safety.
A source told the Irish Examiner this is a key concern, as the wording has the potential to undermine two years of Brexit talks.
The Government decided at approximately 8.30pm to adjourn the emergency cabinet meeting until 10.30pm in order to allow time for Mr Juncker and Ms May's talks in Strasbourg to conclude.
However, it is understood Government ministers will be given a likely agreed wording of the "unilateral" declaration on the backstop the UK is seeking before the cabinet returns tonight, leading to yet another make or break Brexit moment.
One source said while it is "too early to say if a deal is here, you could see a direction towards a deal and further progress tonight".
As the political drama took place in Dublin, Ms May was understood to be preparing to give a statement just after 10pm in Strasbourg.
Similarly, the hard-line Brexiteer Conservative party group the European Research Group is meeting in London and DUP leader Arlene Foster is understood to be in London meeting senior Conservative party members and UK government officials.
The European parliament Brexit negotiation group is also believed to be meeting in Brussels to discuss the ongoing developments.
At the time of publication, the planned three days of Brexit votes in the House of Commons - existing deal on Tuesday, ruling out no deal on Wednesday and voting on a potential extension on Thursday - are still scheduled to take place.