Three years ago, when Kristin Crowley became the first female chief in the history of the Los Angeles Fire Department, she was lauded as a force for stability.

“There is no one better equipped to lead the L.A.F.D. at this moment than Kristin,” the mayor at the time, Eric Garcetti, said of the 22-year veteran of the department. “She’s ready to make history.”

Now, as Los Angeles reels under an extended onslaught of wind-driven wildfire, its fire chief is being buffeted by challenges in and outside her ranks, tension with City Hall and questions about her department’s preparedness. The fires, which are still unfolding on the city’s west side and in the community of Altadena outside the city, have so far leveled nearly 40,000 acres and claimed at least 27 lives.

Last week, complaints about funding for her department boiled over into a public dispute between Mayor Karen Bass and Chief Crowley. This week, veteran fire managers charged that she and her staff should have positioned more engines in advance in high-risk areas like Pacific Palisades, where the fires began on Jan. 7.

At a news conference, she struggled to explain why an outgoing shift of about 1,000 firefighters was not ordered to remain at work last Tuesday as a precaution amid extreme red-flag conditions. “We surged where we could surge,” she said.

A Jan. 13 letter signed by unnamed “retired and active L.A.F.D. chief officers” accused her of a host of management failures and called for her to step down. “A large number of chief officers do not believe you are up to the task,” the five-page letter read in part.

In an email on Thursday, a fire department spokesperson said that the chief was “focused on mitigating the fires” and unable to respond to the letter. The chief has repeatedly emphasized the progress her crews are making.

“Our firefighters are doing an incredible job,” she said in a news briefing on Thursday, as a continuing air and ground assault brought hot spots in Pacific Palisades closer to containment. “As their chief, I’m extremely proud of the work that our people did and continue to do.”

With thousands of evacuees clamoring to return to the remains of their homes and more red-flag wind conditions in the forecast, many civic leaders in Los Angeles have reserved judgment.

“This was a huge natural disaster not any single fire chief could have prevented, whether they had unlimited resources and money,” said Corinne Tapia Babcock, a member of the Los Angeles Fire Commission, which oversees the department and its chief. “You cannot attack a single person for a situation that is this catastrophic.”

Zev Yaroslavsky, a former member of the Los Angeles County Board of Supervisors and City Council, said that “an accounting should and will take place when the smoke clears.”

“But these issues can’t be resolved while the city’s on fire,” he added.

Other civic leaders predicted that, sooner or later, the chief would be held to account.

“She’ll be gone in six months,” said Fernando Guerra, who directs the Center for the Study of Los Angeles at Loyola Marymount University.

Even before the fire, the chief faced strong political challenges, Dr. Guerra said. Her appointment in early 2022 by the prior mayor, Mr. Garcetti, was seen as an attempt to steady the department after years of complaints of harassment and discrimination raised by female L.A.F.D. firefighters.

But it challenged the male-dominated culture of the department, Dr. Guerra noted, as did the election later that year of Ms. Bass as the new mayor. Like other top managers in Los Angeles city government, fire chiefs are mayoral appointees and can be replaced by a new administration. Ms. Bass kept her on.

Even with more than two decades with the department, Chief Crowley was still new in her post — just beginning to develop a base of support — when the Palisades burst into flames last week.

As the fire turned into a catastrophe, critics of Mayor Bass, including Patrick Soon-Shiong, the owner of The Los Angeles Times, and Elon Musk, the owner of X, the social media platform, charged that the fire department had been underfunded. A December memo from Chief Crowley surfaced, in which she warned the fire commission that a $7.9 million cut in firefighter overtime and the elimination of dozens of civilian positions had “severely limited” the department’s ability to respond to large-scale emergencies.

Ms. Bass had approved a budget last June for the fire department’s current fiscal year that was $23 million less than the prior year’s. But a new contract with the firefighters’ union led to raises, and the final fire budget was actually $53 million more than last year’s.

The claims about underfunding sparked a dayslong dispute with the mayor and her allies. By the end of last week, Chief Crowley had doubled down, telling a local Fox News affiliate that she felt the city government had failed the fire department.

Within hours, she and Ms. Bass — facing criticism herself for having been out of the country when the Palisades fire started — disappeared into the mayor’s office for so long that they missed an evening news briefing. Outside the closed doors, the mayor’s staff repeatedly denied an erroneous report from a British news outlet that the chief had been fired.

By Saturday morning, the mayor and the chief were projecting a unified front, though the tension was apparent. “The chief and I are in lock step,” Ms. Bass said. “And if there are differences that we have, we will continue to deal with those in private.”

But criticisms of the chief flared again this week amid reports in The Los Angeles Times that the firefighting force that was on duty when the Palisades fire started could have been much larger. In years past, the department often paid outgoing shifts overtime to stay at work in times of alarming wind forecasts and tinder-dry conditions.

Internal documents reviewed by The New York Times also showed that the department’s plan on the day of the fire called for advance positioning of only nine additional fire trucks — near Hollywood, the Santa Monica Mountains and elsewhere in the San Fernando Valley — but none in Pacific Palisades.

Patrick Butler, a former L.A.F.D. assistant chief who is now chief of the Redondo Beach, Calif., fire department, said that positioning firefighters and equipment near fire zones in significant numbers well in advance during periods of high wildfire danger has long been a key strategy in the department. “It’s unfathomable to me how this happened, except for extreme incompetence and no understanding of fire operations,” he said.

Others said the fire chief should have kept both the incoming and outgoing shifts of firefighters on duty before the fire as a precaution.

“I can’t speak to why she didn’t exercise it, but it’s a known tactic and it would have doubled the work force,” said Rick Crawford, a former L.A.F.D. battalion chief who is now the emergency and crisis management coordinator for the U.S. Capitol. “I’m not saying it would have prevented the fire, or that the fire wouldn’t have gotten out of control. But she lost a strategic advantage by not telling the off-going shift, ‘You shall stay and work.’”

In the letter purportedly signed by current and retired officers in the department, there were complaints that Chief Crowley had also failed to temporarily call back experienced fire commanders who had recently retired.

“While no one is saying that this fire could have been stopped, there is no doubt among all of us that if you had done things right and prepared the L.A.F.D. for an incident of this magnitude, fatalities would have been reduced, and property would have been saved,” they wrote.

Sharon Delugach, a member of the Los Angeles Fire Commission, said that rumors of disgruntlement within the department had been on the radar but had not risen to the commission’s formal attention before the fires broke out.

Much of the criticism, she said, seemed to reflect sentiments of sexism or homophobia — Chief Crowley is the first lesbian to lead the department — or came from those who were unhappy about change.

Whatever the source, Ms. Delugach said, the timing of the latest dissent is not ideal when many outside of the department seem intent on scoring political points.

“I’m sure they do have very legitimate concerns and I’m sure everybody in the department is there for the right reason,” Ms. Delugach said of the internal criticism. “It’s a shame all this dirty laundry is being aired in the moment of fire.”

Ms. Delugach predicted that Chief Crowley’s future would hinge less on internal and external critiques than on her relationship with Ms. Bass.

“It’s whether she and the mayor can work together, that’s the real question,” Ms. Delugach said. “I hope they can.”

Rachel Nostrant, Nicholas Bogel-Burroughs, Kate Selig and Katie Benner contributed reporting.