With the turmoil surrounding Mayor Eric Adams casting uncertainty onto this year’s mayoral race, some Democratic leaders in New York City have been trying to persuade Adrienne Adams, the City Council speaker, to enter the race.

Ms. Adams, the first Black woman to lead the Council, has not made up her mind. But she said in an interview that a decision is close and that she filed paperwork on Wednesday establishing a citywide campaign committee to run for mayor.

Ms. Adams, who is not related to the mayor, said she intended to make a final decision after her State of the City address next Tuesday.

“I didn’t seek this out, but it’s been in the back of my mind for quite a while, particularly in working with this administration,” Ms. Adams said. “But it hasn’t been until this crescendo, this crisis, that it’s like a neon sign flashing in front of my face that somebody has to be here to work to save the soul of this city.”

Ms. Adams, 64, is not well known outside the circle of those who follow city politics, and she would face immediate fund-raising challenges to catch up to Democratic rivals who have been in the race for months. She is also battling history: The four other City Council speakers who have run for mayor were all unsuccessful, and New York City has yet to have a female mayor.

But she is seen by her allies as an antidote to the ethical, legal and management issues facing Mr. Adams, as well as someone who could gather a diverse coalition to compete against the former Gov. Andrew M. Cuomo if he enters the race for mayor, as expected.