LONDON - British Prime Minister Theresa May will set out a timetable for her departure in early June after the latest attempt to get her Brexit deal approved by parliament, the chairman of a powerful Conservative committee said on Thursday.

Three years after Britain voted to leave the European Union, there is little clarity over when, how and even whether Brexit will happen, prompting some in her party to call for a new approach to the country's biggest policy shift in more than 40 years.

May has promised to step down after her Brexit deal is approved by lawmakers. But many in her party want her to set out clearly when she will quit if the agreement is rejected for a fourth time, and others are demanding her immediate departure.

"The prime minister is determined to secure our departure from the European Union," Graham Brady, chair of the 1922 Committee that can make or break party leaders, said following a meeting between his committee's executive and May in parliament which he described as a "very frank exchange".

The government has said lawmakers will be able to debate and vote on the Withdrawal Agreement Bill, the legislation required to enact May's Brexit deal, in the week starting June 3.

"We have agreed that she and I will meet following the second reading of the Bill to agree a timetable for the election of a new leader," Brady said, adding that the conversation would take place whether the bill was passed or not.

May, who became prime minister in the chaos that followed the 2016 referendum when Britons voted 52% to 48% to leave the EU, survived a no-confidence vote of her Conservative lawmakers in December.

Under current party rules, she cannot be challenged again for a year, but some on Brady's committee had pushed for those rules to be changed in order to try to force her out earlier if she refused to set out a clear departure date.

Boris Johnson, the face of the campaign for Britain to leave the European Union, said he would stand as a candidate to replace May as Conservative leader.