Senior Conservatives are set to hold further talks on whether to change party rules to enable an early leadership challenge to Theresa May.
Under current party rules, MPs cannot mount a fresh challenge against Mrs May until December – 12 months after the last failed no confidence vote in her.
On Tuesday, the 1922 committee of backbench Tories began discussions on a rule change.
It comes amid growing pressure for the PM to name the date of her departure.
Last month, she pledged to stand down if and when Parliament ratified her Brexit withdrawal agreement.
But some long-standing Leave campaigners want her to announce a date now, irrespective of whether a Brexit deal is completed.
Some of those who want to change the Conservative rules say another vote of confidence should be permitted after six months, rather than a year, if a relatively high number of MPs – 30% or 40% – call for it.
But other members of 1922 Committee are sceptical of long term rule changes to address a very specific circumstance.
They are also worried about showing further party divisions ahead of the potential European elections on 23 May.