LONDON — Battling to hold on as prime minister of Britain after losing her majority in Parliament in the election last week, Theresa May shored up her position on Monday by expressing contrition to fellow Conservative Party lawmakers and promising to consult them more.

“I got us into this mess, I’m going to get us out of it,” Mrs. May told the lawmakers, according to several who attended a private meeting with her in Parliament on Monday. They said she got a generally positive reception.

Mrs. May met for more than an hour on Monday with the Conservative caucus in the House of Commons, known as the 1922 Committee, after shaking up her cabinet over the weekend to broaden its appeal to her party’s rank and file.

To survive for long as the head of a minority government, she will need all of the caucus members’ votes. The defections of even a few could block major legislation and force her to resign, or she could be toppled through a party leadership challenge.