Britain's justice secretary has signaled the government might take a more conciliatory approach to Brexit as Parliament prepares for another round of votes on alternatives to Prime Minister Theresa May's withdrawal deal with the European Union.

The House of Commons is set to debate options on Monday in hopes of finding an approach that can command a majority. Lawmakers rejected her Brexit deal with the European Union for a third time last week, though the agreement failed by fewer votes - 58.

David Gauke told the BBC on Sunday the government "would need to consider very carefully the will of Parliament" though he didn't pledge to support any plan lawmakers might back.

Amid reports May is planning a fourth vote on her withdrawal, Gauke said May is "reflecting on her options."