The chairman of Britain's Conservative Party is urging Parliament to back an unpopular withdrawal agreement as British and European Union officials seek a breakthrough on the Brexit impasse.

Britain's Prime Minister Theresa May gives a speech in Grimsby, north east England, Friday March 8, 2019. British lawmakers are due to vote for a second time Tuesday on the deal, which they overwhelmingly rejected in January. (Photo: AP)

Brandon Lewis on Saturday warned recalcitrant lawmakers, including many in his own party, that if the government's withdrawal plan is voted down Tuesday it is possible Britain will end up staying in the EU.

"We need to win that vote," he told BBC, warning that a defeat for the withdrawal plan agreed after two years of negotiations would lead to a totally unpredictable situation.

"Nobody quite knows where we will end up — whether we end up with a hard Brexit with no deal... but there is also a risk with Parliament that we end up with no Brexit at all," he said.

British lawmakers are due to vote for a second time Tuesday on the deal, which they soundly thrashed in January. If Parliament throws out the deal again, lawmakers will vote on whether to leave the EU without an agreement — a prospect with little support in Parliament — or to ask the EU to delay Brexit beyond the scheduled March 29 departure date.

Prime Minister Theresa May has also warned that a second defeat to her bill could thwart the Brexit process altogether. She has made passage of the bill the centerpiece of her tenure.

But there is no sign of progress in the crisis talks. EU leader are adamant in their refusal to make alterations to the legal document that would govern Britain's withdrawal from the 28-nation bloc

British officials have rejected the latest proposed compromise from Europe as a rehash of old ideas that have already been rejected, while EU leaders have rejected May's effort to cast them as intransigent, with chief EU negotiatior Michel Barnier saying he is not interested in playing the "blame game."