LONDON — Prime Minister Theresa May said on Sunday that she would hold more talks in Brussels this week over Britain’s withdrawal from the European Union while she battles twin threats at home: a possible no-confidence vote on her leadership and new resignations from her fractious cabinet.

Mrs. May faces a perilous few days after her draft agreement provoked two cabinet resignations and such widespread objections from lawmakers of all political persuasions that the document looks unlikely to win Parliament’s approval.

“This isn’t about me,” Mrs. May said on Sky News. “This is about the national interest. The next seven days are critical.”

Since Britons voted in 2016 to quit the European Union, Mrs. May’s Conservative Party has been split between those who want to keep close economic ties with the bloc and a more hard-line faction that wants a clean break.