Senior Conservatives are expected to hold further discussions on whether to change the party rules to enable an early leadership challenge to Theresa May.
MPs in the influential Tory backbench 1922 Committee met in Westminster on Tuesday amid growing pressure for the Prime Minister to name the date of her departure.
The meeting took place against a backdrop of a swelling of discontent at Mrs May's leadership among Tory grassroots.
As many as 70 local association chiefs have signed a petition supporting an unprecedented vote of confidence in her leadership, according to reports, and it is thought some MPs may have used the two-week Easter break to find "renewed energy" for plans to remove the Prime Minister from office.
- ITV News Political Correspondent Paul Brand reports on what he says is "renewed energy" within some elements of the Conservative Party to remove Mrs May from office
- What rules could be changed?
Under current party rules, MPs cannot mount a fresh leadership challenge until 12 months after the last one.
In December, Mrs May survived a vote of no confidence by a vote of 200 to 117.
However, amid growing frustration over the latest delays to Brexit, some MPs now want the rules to be rewritten to allow another challenge after just six months, permitting another vote as early as June.
One member of the 1922 Committee, joint executive secretary Nigel Evans, has called publicly for Mrs May to go “as soon as possible”.
- Why do May's own MPs want her to out?
Many Brexiters within the Conservatives are unhappy with Mrs May's handling of the Brexit talks with the EU and the delays to the country's exit.
It is feared within the party that they will suffer badly at upcoming Local and European elections and it is hoped the Tories would perform better without Mrs May at the helm.
Traditional Tory voters could be swayed to vote for Nigel Farage's new Brexit party, which would be a devastating blow to the Conservatives, due to Mrs May's failure to take the UK out of the EU and her extension of Article 50.
Mrs May has lost three separate votes on her Brexit deal in Parliament by large majorities, a sign her power is waning.
Additionally, Backbenchers see Mrs May's cross-party talks with Labour over Brexit as a betrayal and a sign that they the country will end up with a softer Brexit than they desire.
- Will the Prime MInister hang on?
It is reported that there will be further discussions ahead of the weekly meeting of the full 1922 Committee on Wednesday.
Ahead of Tuesday’s talks, the committee chairman Sir Graham Brady met privately with Mrs May, when he is reported to have told her MPs want her to announce when she is going.
- Do all Tory MPs want May out?
Some members of the 1922 Committee were reported to have pushed back at Tuesday’s meeting, questioning what a fresh leadership contest at the current time would achieve.
Richard Harrington MP said a new leadership election would be "disastrous", while Rory Stewart believes such a situation will not solve anything within the party.