"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".
He acknowledged that more work was needed to get the United Kingdom ready for Brexit on March 29, telling the BBC's Andrew Marr Show there are "still steps that are currently being put in place" but "there is steady work that is going on, 10,000 civil servants that are now focused on this" and the Border Force was "ramping up" its staff.
Jeremy Corbyn has accused May of a "cynical" attempt to run down the clock before the March 29 Brexit date in order to leave MPs with a stark choice of accepting her deal or crashing out of the European Union without any agreement.
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.
May wants to win over lawmakers in her Conservative Party with changes relating to the Northern Irish border, but the EU has refused to reopen that part of the deal and instead wants May to pursue a compromise with the main opposition Labour Party by agreeing closer UK-EU ties. "That isn't right in terms of the respect for parliament", said Starmer.
"There needs to be a day when Parliament says that's it, enough is enough".
"It's this blinkered approach that's got us to where we are, with her never wanting to see where the real majority is in parliament".
Mrs May's Brexit deal - which she spent months negotiating and had agreed with the European Union - covers the terms of the UK's divorce and the framework of future relations. The new pledge would be for a repeat of this process by February 27.
He told the Sophy Ridge on Sunday programme that it would lead to a "very hard border" on the island of Ireland and is contrary to the Good Friday Agreement, the peace deal he helped negotiate which brought an end to The Troubles.