New Yorkers have grown accustomed to being inundated with well-intentioned warnings from city and state leaders, for everything from incoming snowstorms to virus outbreaks.

But as the skies darkened dramatically over New York City on Tuesday evening, the air suddenly rich with acrid smoke, Mayor Eric Adams and Gov. Kathy Hochul made no public appearances about the worsening conditions, limiting their communications to news releases and posts on Twitter.

It was not until Wednesday morning, roughly 12 hours after the air quality reached historically unhealthy levels, before Mr. Adams and Ms. Hochul addressed reporters to discuss the health crisis.

Mr. Adams drew almost immediate criticism over his response; Ms. Hochul was mostly spared. They were among the leaders of cities across the Eastern Seaboard who were suddenly left to grapple with a situation they had never dealt with before, as air quality worsened to levels not seen since the worst effects of wildfires in California and Oregon.

In New York City, the air quality index hit 413 on Wednesday, the highest level ever recorded, sending more patients than usual to city hospitals with respiratory problems and prompting Broadway shows and a Yankees game to be canceled.

Mr. Adams and Ms. Hochul, Democrats in a state with an outspoken left-wing of the party, are not strangers to crises, from the pandemic to heightened crime and the influx of tens of thousands of migrants from the southern border.

But some health experts and elected officials in New York City suggested that Mr. Adams and Ms. Hochul should have moved more quickly to alert residents to the hazards posed by the smoke, to distribute high quality masks and to urge more people to work from home.

Wildfire smoke at high levels can cause symptoms like stinging eyes or coughing for people without underlying conditions.

But for those who are most vulnerable, especially those with respiratory issues like asthma, even brief exposures can have more serious and immediate ramifications, as toxins in the smoke can trigger inflammation and worsen existing health problems.

Rebecca Bratspies, the director of the Center for Urban Environmental Reform at the City University of New York School of Law, said that masks were distributed too late, after the worst air quality conditions had passed.

She said that she had been watching reports about the wildfires in Canada since last weekend and the city should have been better prepared.

“When the mayor says there’s no game plan for this — of course there is,” said Ms. Bratspies, who serves on the city’s Environmental Justice Advisory Board.

Mr. Adams strenuously defended the city’s response and said that officials were doing their best to respond to a new and unpredictable threat.

“What we should really try to prevent doing is to give any indication that this administration did not proactively respond and did not move in the right direction to let New Yorkers know,” Mr. Adams told reporters on Wednesday morning.

By Thursday, the mayor’s tone became more strident. He asked reporters if he should also be prepared if a “meteor fell to the planet Earth.” (The White House does have a plan for a meteor strike.)

“So if you want to play — ‘Why didn’t you know every problem that this is going to create?’ — that’s up to you,” the mayor said. “I know how well this team responded.”

Mr. Adams, who is known for keeping a relentless schedule of public appearances, sought to show his hands-on approach by visiting a public housing building on Wednesday night to distribute masks.

But the city’s commissioner for emergency management, Zach Iscol, acknowledged on Wednesday that the city did not have an “off-the-shelf plan” for a smoke emergency, even though it has other plans for unlikely events like a nuclear attack.

“That’s something that we are now developing,” he told reporters.

Dr. Jay Varma, director of the Cornell Center for Pandemic Prevention and Response and a health adviser under former Mayor Bill de Blasio, said that the health crisis showed the need for the state and city to create early warning systems to alert residents about the risks of wildfire smoke in advance, like they do with coastal storms, and to consider solutions to improve air quality when it is poor, such as limiting car traffic as other cities do, including Beijing and Mexico City.

The state’s Department of Environmental Conservation first posted an advisory warning about elevated levels of fine particulate matter in certain parts of the state on June 1.

On Tuesday afternoon, the governor’s office issued a news release announcing that the wildfires were creating hazy conditions in New York City and elsewhere, urging residents to limit exposure and saying state experts were monitoring the situation.

On Wednesday morning, as many New Yorkers woke up to a thick blanket of haze, the governor spoke to reporters in Albany about the situation, saying it was “an emergency crisis” and warning it could last several days.

Asked about the wisdom of declaring a state of emergency, Ms. Hochul said that it was unnecessary.

“A state of emergency is a mechanism you use when there’s something you can do about it,” she said. “We don’t have a lot we can do about the circumstances for contaminated toxic air coming into our airspace, so there’s not a need for deploying resources or bringing money to the table.”

On Wednesday evening, Ms. Hochul held an impromptu briefing in Albany to provide further updates and announced that the state would make one million Covid masks available from its stockpile. The masks, she said, would be distributed in subway stations, state parks, at state facilities and directly to local governments.

Dr. Varma said that he was glad that Ms, Hochul was distributing masks, but that some New Yorkers needed them more urgently than others.

“I would like to have seen that the priority was going to areas with higher rates of asthma, which basically overlap with racial and economic disparities,” he said.

On Thursday, as scrutiny of Mr. Adams’s response mounted, Ms. Hochul sought to fend off any criticism of the state’s actions by noting state officials began sending advisories as early as last week.

She said there was no way of knowing that the air quality would deteriorate so precipitously.

“Six days ago, we started giving out our announcements to be prepared,” the governor said during another briefing in Albany. “We were monitoring.”

The explanations from the governor and Mr. Adams did little to allay criticism, especially of the mayor. Lincoln Restler, a City Council member from Brooklyn, complained on Wednesday afternoon that the city had “not taken a single proactive step to protect New Yorkers,” other than suspending outdoor activities at schools.

Brad Lander, the city comptroller and a frequent critic of the mayor, said in an interview that the city should have been prepared with a plan to respond because California had experienced similar events for years.

“We just came through a crisis that was all about masks, ventilation and air quality,” he said in reference to the pandemic. “We were too slow to deploy them at a moment when they’re urgently needed.”

And Melissa DeRosa, who was a top aide to former Gov. Andrew M. Cuomo, blamed both federal and state leaders for not communicating quickly enough with New Yorkers.

“Would be nice if there was a steady stream of information from the federal and state governments telling people what is going on,” she wrote on Twitter.

Dana Rubinstein contributed reporting.