| 22 Jan 2019, 00:00 | Update : 22 Jan 2019, 08:28
Theresa May has scrapped the £65 fee millions of EU citizens were going to have to pay to secure the right to continue living in the UK after Brexit.
She also vowed to seek changes to the Irish backstop from the EU, reports BBC.
But she again rejected calls to rule out a "no-deal" Brexit - and warned another EU referendum could threaten the UK's "social cohesion".
Conservative rebels and Labour accused her of being in denial about the scale of opposition to her Brexit deal.
May had been forced to make the statement setting out her plan for how to proceed after MPs rejected her Brexit deal with the EU by 230 votes last week - her "plan B".
MPs are due to vote on a modified version of the deal next Tuesday, although she gave few details about how it would be changed.
Between now and then, MPs will table a series of amendments - proposed changes to the PM's deal - in an attempt to force through alternatives to her Brexit deal. The Commons Speaker John Bercow will choose which amendments are put to a vote.
May promised to seek the views of Northern Ireland's Democratic Unionist Party - who keep her minority government in power - and others on the proposed Irish backstop.
She said she would then "take the conclusions of these discussions back to the EU".
She said she was exploring potential "movement" on the backstop that could secure the backing of a majority of MPs, with the aim of addressing concerns that it could become permanent and threaten the integrity of the United Kingdom.
The backstop is the "insurance policy" in the withdrawal deal, intended to ensure that whatever else happens, there will be no return to a visible border between Northern Ireland and the Irish Republic after the UK leaves the EU.
Both the UK and the EU believe that bringing back border checks could put the peace process at risk.
The prime minister attacked the Labour leader for refusing to take part in talks with her on the way forward.
She promised to take a more "flexible, open and inclusive" approach to involving MPs and the Scottish and Welsh governments, in negotiating a future relationship with the EU - once her Brexit deal has been approved.
But Labour's Yvette Cooper asked why MPs could not be given a greater say now.
"Why not put to Parliament some votes on her red lines, including a customs union, otherwise how can any of us believe a word she says?"
Conservative rebel Sarah Wollaston, who backs another referendum, tweeted that it was "like last week's vote never happened".