In a pronounced shift in tactics, Gov. Kathy Hochul of New York on Thursday forcefully urged President Biden to respond to the influx of migrants arriving in the state, underscoring the urgency of a situation that has vexed Democratic leaders for months.

Unlike Mayor Eric Adams of New York City, the governor has taken pains to avoid overtly criticizing the president’s response, choosing instead to communicate with Mr. Biden and his staff behind the scenes.

But the governor’s 10-minute address, live streamed from Albany, laid the blame directly at the door of the White House. She noted that the Biden administration has failed to respond to her call to expedite work permits for newcomers and turn more federal properties into emergency shelters, saying, “We’ve managed thus far without substantive support from Washington.”

“New York has shouldered this burden for far too long,” the governor, a Democrat, said in her most direct appeal to federal officials. “There does not appear to be a solution to this federal problem any time soon. This crisis originated with the federal government, and it must be resolved through the federal government.”

More than 100,000 migrants have traveled to New York City from the southern border over the past year, and more than half of them have taken refuge in the city’s shelters, straining the system. Though Ms. Hochul and Mr. Adams have sought to display a united front, the surge has led to disagreements between them over the response, some of which burst into public view in letters between state and city officials last week.

The crisis has also begun to prompt criticism of Mr. Biden by elected officials from his own party in states and cities where migrants have arrived en masse.

In Massachusetts, Gov. Maura Healey, a fellow Democrat, also called for expedited work permits and pleaded for Mr. Biden to intervene earlier this month, describing the situation as “a federal crisis of inaction.” And on Thursday, six mayors from cities in Pennsylvania, including Philadelphia and Pittsburgh, wrote Mr. Biden to urge him to expand protections and work authorization for migrants.

In a statement, a White House spokesman said the administration was coordinating closely with New York City and the state, noting a recent visit to the city by Tom Perez, a senior Biden adviser, and said “only Congress can fix the broken immigration system.”

Directly addressing New Yorkers on Thursday, Ms. Hochul insisted that the way out was to accelerate migrants’ ability to work legally while they awaited the outcome of their asylum cases, in order to get them out of shelters and on their feet financially. She said she sent a letter to Mr. Biden on Thursday pressing for four executive actions Mr. Biden could take to alleviate the situation.

Ms. Hochul also announced the launch of a new state program that will help connect employers across the state with asylum seekers once they are granted permission to work. She framed the initiative as a potential lifeline for restaurants, farmers and hotels struggling with labor shortages.

“We have countless unfilled jobs that are begging for someone to just take them,” she said. “We are ready to act as soon as these migrants receive work authorization.”

The speech came as Ms. Hochul herself has come under pressure to play a more active role in managing a situation. Ms. Hochul has deployed state resources — over $1.5 billion in aid and nearly 2,000 National Guard members — but has avoided regular news briefings on the topic and has not enacted statewide policy, ceding the public role of crisis manager to the mayor.

Warning the city was nearing a breaking point, Mr. Adams has called on Ms. Hochul to develop a statewide “decompression” strategy to compel other counties to take in migrants.

The mayor’s decision to bus migrants north of the city last spring sparked lawsuits and fierce backlash in Republican-controlled counties. Since then, the 2,000 or so migrants being housed upstate at the city’s expense have mostly been sent to Democratic areas, such as Albany and Rochester.

On Thursday, Mr. Adams praised Ms. Hochul’s demand for more federal aid, but also insisted that the governor needed to go further. He suggested that she use executive orders to prevent other counties from barring migrants sent from New York City.

“Leaving New York City alone to manage this crisis — and abdicating the state’s responsibility to coordinate a statewide response — is unfair to New York City residents who also didn’t ask to be left almost entirely on their own in the middle of a national crisis,” he said in a statement.

The governor has pushed back on the idea of relocating more migrants to the suburbs and upstate, where the crisis has become a political minefield for Democrats, arguing that New York City is best equipped to absorb the influx because of its access to jobs and public transportation.

New Yorkers appear increasingly frustrated by the response from Democrats in power. A Siena College poll released this week found that 82 percent of voters believe the situation has become a “serious problem”; 56 percent also said New York has done enough and should move to slow the flow of migrants.

Tensions have even flared in the liberal stronghold of New York City, where some residents have protested emergency shelter sites in school gyms, soccer fields and underused government buildings in their neighborhoods. Even news this week that Floyd Bennett Field, a far-flung former airfield in southeast Brooklyn, would be used to house more than 2,000 migrants provoked pushback from Democratic legislators who represent the area.

With migrants continuing to arrive, Ms. Hochul, along with the mayor and some labor unions, has repeatedly reiterated the need to shift the government’s response away from shelters by fast-tracking work permits for migrants.

“Our quest continues to squarely tell the White House: Let them work,” Ms. Hochul said on Thursday.

To expedite the process of helping migrants enter the work force, state officials said the administration would reach out to employers in a variety of sectors to see which companies and regions had the greatest demand for migrant labor. Migrants would be directed to list their qualifications and preferences for types of work and locales, and then the state would attempt to serve as matchmaker.

Jackie Bray, commissioner of the New York State Division of Homeland Security and Emergency Services, said the effort was part of the administration’s goal to help migrants build stable lives and find permanent homes.

“What the state is going to do here is to assist with resettlement, not resheltering,” she said, noting that migrants had already traveled great distances to reach New York, in some cases against their will.

Asylum seekers need to wait a minimum of 180 days after they file their application, sometimes even longer, before being allowed to work legally, creating a backlog that prevents migrants from working in the meantime or leads them to the underground economy. Some migrants may take weeks or months to file an application after they arrive in the United States as they search for legal help.

Ms. Hochul and Mr. Adams have also called for the expansion of the Department of Homeland Security’s authority to grant temporary protected status to asylum seekers fleeing civil unrest, environmental disasters or other catastrophic but nonpermanent conditions. This status, which applies to 16 countries, including El Salvador and Ukraine, allows migrants to legally work and apply for permanent status without fear of deportation.

The status has its limitations as a policy tool: Only those who are in the United States at the date the government specifies are eligible for the benefit, which includes work permits.

Some immigration advocates are pressuring the Biden administration to make the temporary benefit available to Guatemalans and people from the Democratic Republic of Congo, noting the potential economic benefits of incorporating migrants into the legal labor market. But others worry that broadly granting temporary status could incentivize more people to make the perilous journey, exacerbating the situation on the ground.

It’s not clear that this benefit would get migrants work authorization any faster than if they applied through the asylum process: The median time the government is taking to process applications for temporary protected status is 13 months, according to U.S. Citizenship and Immigration Services.

Eileen Sullivan contributed reporting.