When the behind-closed-doors session is over, the 317 Tories are due to start voting in the no-confidence contest.
May refused to put an exact date on when she will stand down, despite calls for her to go as soon as Britain formally leaves the EU.
No-confidence vote in May begins
Earlier, MP Graham Brady said the threshold of 48 letters from lawmakers needed to trigger a leadership vote had been reached. Brady chairs the party committee that oversees leadership contests.
Many lawmakers have been growing angry with May over her handling of Brexit.
If she loses the vote of party legislators, May must step down. If she wins, she can't be challenged again for a year.
All 315 Tory legislators can vote on the confidence motion.
May needs 158 votes to win. If she loses, she must resign and a party leadership contest is held in which she is barred from running.
All other Conservative lawmakers can run.
Conservative leadership contests have two parts.
After candidates come forward, Conservative lawmakers vote first. The candidate with lowest number of votes drops out and voting continues until there are two contenders left.
The final two candidates are put to a vote of the full party membership across the country.
In the last leadership contest in 2016, members never got to vote because all the candidates dropped out but one: May.
May remains Prime Minister and party leader until a replacement is chosen. The winner of the vote becomes Conservative leader and prime minister, without the need for a national election.
- AP