The Prime Minister avoided confirming a date for her resignation but said she would do so after presenting Brexit legislation to the Commons.
Theresa May has agreed she will set a timetable for her departure as Prime Minister after the initial stages of Brexit legislation have been completed.
Mrs May met with the 1922 committee on Thursday to discuss increasing demands for her to confirm when she intends to quit as party leader.
She previously offered to step down once a Brexit deal had been delivered on, but did not specify a date.
Now the committee chair Sir Graham Brady said she agreed to meet again to decide a timetable in early June, following the second reading of the Withdrawal Agreement Bill.
“The Prime Minister is determined to secure our departure from the European Union and is devoting her efforts to securing the second reading of the Withdrawal Agreement Bill in the week commencing June 3 2019 and the passage of that Bill and the consequent departure of the United Kingdom from the European Union by the summer,” Sir Graham said in a statement.
“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 of the Conservative and Unionist Party.”