"The government will commit that if the meaningful vote, in other words the deal coming back, has not happened by the 27th of February, then we would allow a further motion - votable in Parliament - to take place, to give that sense of assurance as to the process moving forward", he told the BBC's "Andrew Marr Show".
Mrs May described discussions with European Union leaders in Brussels as "robust but constructive" and insisted she was determined to "negotiate hard" over the coming days to secure legally-binding changes to the Agreement which will render it acceptable to Parliament.
"There needs to be a day when Parliament says that's it, enough is enough".
British International Trade Secretary Liam Fox and Swiss Federal Councilor Guy Parmelin, who heads the Federal Department of Economic Affairs, finalized the deal between their countries in Bern on Monday.
"I think that gives that sense of timetable, clarity and goal on what we are doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has".More news: Dramatic rescue of baby underway in Durban
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In today's Brexit Brief, British Prime Minister Theresa May responds to the Labour party with an offer of talks, MPs gear up for a Brexit debate on Thursday and Germany experiences job losses.
British businesses are also stockpiling goods as March 29 draws nearer, when the United Kingdom will by default crash out of the block if a withdrawal agreement can not be reached.
Britain's economic slowdown should not be blamed entirely on Brexit, British Trade Minister Liam Fox said on Monday after data showed the economy a year ago grew at its slowest since 2012.
A number of government ministers will also be meeting their counterparts across the continent this week, in order to underline Mrs May's determination to achieve a deal. The backstop is the main obstacle to securing agreement on the terms of Britain's withdrawal from the EU.