Is Letitia James Running for New York Governor?

“A number of individuals have approached me with respect to running for higher office,” she said, even as she repeatedly insisted that her focus was on her current job.

But asked to characterize those conversations, Ms. James did not shy away.

“That I should consider it because of my leadership, because of my ability to speak truth to power, because of my experience and because of my ability to unite the state,” she said. “I’m still focused on the office of attorney general, but I thank them for their comments.”

Her comments came after she spoke briefly at a gathering of the Brooklyn Democratic Party at Junior’s, a restaurant known for cheesecake and political events.

The scene there offered one of the most vivid illustrations yet of how the Democratic primary has begun to take shape in the past week, with the nascent contours of a campaign trail coming into view.

Ms. Hochul, the state’s first female governor, was there as well, part of her breakneck public schedule as she also moves aggressively to try to cement a huge fund-raising advantage in advance of the primary. She spoke before both Ms. James and Jumaane D. Williams, New York City’s public advocate, who announced this week that he had formed an exploratory committee and was considering his own run. (“Great job as public advocate!” Ms. Hochul cracked wryly.)

Ms. Hochul, Ms. James and Mr. Williams made the rounds through a room packed with party activists and elected leaders who clamored for selfies and hugs in between bites of scrambled eggs and sips from precariously balanced coffee cups. Mayor Bill de Blasio, who is also thought to be weighing a run, also dropped by, a day after he and the others were at a gathering of Bronx Democrats.

It is possible that Ms. James may not ultimately challenge Ms. Hochul. She does not have a history as a strong fund-raiser, though her allies are hopeful that as the potential first Black female governor in America, she would attract national attention and support should she run. She would also have to give up her current job to run for governor, and she might prefer to seek another term as attorney general instead — boosted, perhaps, by the attention her recent activity has attracted.