Mrs May’s gamble could buy her more time in Number 10 as she continues to face pressure over her leadership.
Sir Graham Brady, chairman of the Tory backbench 1922 Committee, had urged the prime minister to set out a clearer timetable for her departure from office during two meetings this week.
But Mrs May refused, instead indicating that the EU withdrawal agreement bill will go back to the Commons.
Leaving the meeting, Sir Graham suggested the delay was to allow Mrs May one last push to get her Brexit deal through Parliament before the European elections, which are expected to be another brutal defeat for Conservative candidates.
He said: "The executive is very keen to meet the Prime Minister and will have a full opportunity to discuss and to reach whatever conclusions it wishes to reach next week.
"It's my understanding it's the Government's intention to bring a second reading of the Bill forward in the near future, certainly the intention is before the European election takes place.
"Personally I hope the Bill will be brought forward in a form which contains elements of the Political Declaration brought forward that would obviate the need ever for the Irish backstop to apply."
Sir Graham would not confirm whether he was seeking a departure date from Mrs May at the meeting next Wednesday.
But the Tory MP indicated the Withdrawal Agreement Bill could be brought back next week when he said he expected it "hopefully in the much nearer future" than the elections on May 23.
Leaving the 1922 meeting, Brexiteer MP Nadine Dorries expressed impatience.
She said: "She's not given any decision, there's no timetable and they need to get on with it.
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"We need to make sure we get that final decision soon because everybody needs it."
Conservative MP Alberto Costa told the Press Association Sir Graham expected Mrs May to leave once she got her Brexit deal through Parliament.
He said: "The Prime Minister has been very clear she will step down as soon as the Withdrawal Agreement is passed.
"My understanding is that in respect of the request Graham Brady made two weeks ago... he expects to be given an assurance that her Withdrawal Agreement will once again go before Parliament."