Eric Leroy Adams was sworn in as the 110th mayor of New York City early Saturday in a festive but pared-down Times Square ceremony, a signal of the formidable task before him as he begins his term while coronavirus cases are surging anew.

Mr. Adams, 61, the son of a house cleaner who was a New York City police captain before entering politics, has called himself “the future of the Democratic Party,” and pledged to address longstanding inequities as the city’s “first blue-collar mayor,” while simultaneously embracing the business community.

Yet not since 2002, when Michael R. Bloomberg took office shortly after the Sept. 11 attacks, has an incoming mayor confronted such daunting challenges in New York City. Even before the latest Omicron-fueled surge, the city’s economy was still struggling to recover, with the city’s 9.4 percent unemployment rate more than double the national average. Murders, shootings and some other categories of violent crimes rose early in the pandemic and have remained higher than before the virus began to spread.

Mr. Adams ran for mayor on a public safety message, using his working-class and police background to convey empathy for the parts of New York still struggling with the effects of crime.

But Mr. Adams’s first task as mayor will be to help New Yorkers navigate the Omicron variant and a troubling spike in cases. The city has recorded over 40,000 cases per day in recent days, and the number of hospitalizations is growing. The city’s testing system, once the envy of the nation, has struggled to meet demand and long lines form outside testing sites.

Concerns over the virus caused Mr. Adams to cancel an inauguration ceremony indoors at Kings Theatre in Brooklyn — a tribute to the voters outside Manhattan who elected him. Instead, Mr. Adams chose the backdrop of the ball-drop crowd, which itself had been limited for distancing purposes to just a quarter of the usual size.

Still, his swearing-in ceremony in Times Square, shortly after the ceremonial countdown, was jubilant, and Mr. Adams said he was hopeful about the city’s future.

“Trust me, we’re ready for a major comeback because this is New York,” Mr. Adams said, standing among the revelers earlier in the night.

Mr. Adams, the second Black mayor in the city’s history, was sworn in using a family Bible, held by his son, Jordan Coleman, and clasping a framed photograph of his mother, Dorothy, who died last spring.

As Mr. Adams left the stage, he proclaimed, “New York is back.”

Mr. de Blasio also attended the Times Square celebration and danced with his wife onstage after leading the midnight countdown — his last official act as mayor after eight years in office.

Mr. Adams, who grew up poor in Queens, represents a center-left brand of Democratic politics. He could offer a blend of the last two mayors — Bill de Blasio, who was known to quote the socialist Karl Marx, and Michael R. Bloomberg, a billionaire and a former Republican like Mr. Adams.

Mr. Adams narrowly won a competitive Democratic primary last summer when coronavirus cases were low and millions of New Yorkers were getting vaccinated. The city had started to rebound slowly after the virus devastated the economy and left more than 35,000 New Yorkers dead. Now that cases are spiking again, companies in Manhattan have abandoned return to office plans, and many Broadway shows and restaurants have closed.

With schools set to reopen on Monday, Mr. Adams must determine how to keep students and teachers safe while ensuring that schools remain open for in-person learning. Mr. Adams has insisted that the city cannot shut down again and must learn to live with the virus, and he has been supportive of Mr. de Blasio’s vaccine mandates.

Schools Chancellor: David Banks. The longtime New York City educator who rose to prominence after creating a network of public all-boys schools will lead the nation’s largest public school system as it struggles to emerge from the pandemic.

Police Commissioner: Keechant Sewell. The Nassau County chief of detectives will become New York City’s first female police commissioner, taking over the nation’s largest police force amid a crisis of trust in American policing and a troubling rise in violence.

Commissioner of Correction Department: Louis Molina. The former N.Y.P.D. officer who currently oversees a public safety department in Las Vegas will be tasked with leading the city’s embattled Correction Department and restoring order at the troubled Rikers Island jail complex.

Chief Counsel: Brendan McGuire. After a stint as a partner in a law firm’s white-collar practice, the former federal prosecutor will return to the public sector to advise the mayor on legal matters involving City Hall, the executive staff and administrative matters.

Transportation Commissioner: Ydanis Rodriguez. The Manhattan council member is a trusted ally of Mr. Adams’s. Mr. Rodriguez will face major challenges in his new role: In 2021 traffic deaths in the city soared to their highest level since 2013, partly due to speeding and reckless driving.

Health Commissioner: Dr. Ashwin Vasan. Dr. Dave A. Chokshi, the current commissioner, will stay in the role after Mr. Adams takes office to provide continuity to the city’s pandemic response. In mid-March, Dr. Vasan, the president of a mental health and public health charity, will take over.

Deputies. Lorraine Grillo will be the top deputy mayor, Meera Joshi will be deputy mayor for operations, Maria Torres-Springer deputy mayor for economic development, Anne Williams-Isom deputy mayor for health and human services and Sheena Wright deputy mayor for strategic operations.

On Thursday, Mr. Adams announced that he would retain New York City’s vaccine requirement for private-sector employers. The mandate, which was implemented by Mayor de Blasio and is the first of its kind in the nation, went into effect on Monday.

Even so, Mr. Adams made it clear that his focus is on compliance, not aggressive enforcement; it remains unclear whether he will require teachers, police officers and other city workers to receive a booster shot.

Mr. Adams has also said that he wants to continue Mr. de Blasio’s focus on reducing inequality, even as he has sought to foster a better relationship with the city’s elites.

“I genuinely don’t think he’s going to be in the box of being a conservative or a progressive,” said Christina Greer, an associate professor of political science at Fordham University. “Adams is excited to keep people on their toes.”

Nate Schweber contributed reporting.

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