Theresa May has failed to name a date for her departure from Downing Street after a lengthy meeting with Tory backbench leaders.
Senior figures on the 1922 Committee held talks with the prime minister for some 90 minutes in her Commons office, amid pressure on Ms May to declare when she will stand down.
In a statement, he said: “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 3 June 2019 and the passage of that bill and the consequent departure of the United Kingdom from the European Union by the summer.
“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.”
Sir Graham said he would meet Ms May regardless of whether the bill is passed or voted down.