Mayor Bloomberg and Governor Paterson are scrambling to assure New Yorkers that city and state finances will survive the financial tornado sweeping through Wall Street.

The spate of shocking financial news — the fall of the fourth-largest investment bank in America, Lehman Brothers Holidings; the loss of Merrill Lynch as an independent firm, and the imperiled state of the largest insurer in the nation, American International Group — seemed to take both leaders by surprise.

While insisting that Albany and New York City were prepared for such an emergency, Messrs. Bloomberg and Paterson said it was too early to fully grasp the consequences of the shake-up for their budgets, which are already facing sizable deficits next year.

The most immediate impact of the turmoil is the overnight loss of high-paying jobs — a number that could reach tens of thousands, officials said.

The situation threatens to worsen further, with the cratering of the securitizing loan business, the weakening real estate market, the drying up of merger and acquisition activity and initial public offerings, and the sharp declines in profits posted by remaining securities firms, such as Goldman Sachs.

Messrs. Bloomberg and Paterson emptied their schedules to deal with the unfolding crisis. The mayor canceled his trip to San Francisco, where he was supposed to campaign for Governor Schwarzenegger’s redistricting ballot initiative.

In separate press conferences yesterday, the leaders spoke of grave financial circumstances but also sought to allay fears, insisting that the city and state would be able to cope with the rapidly deteriorating landscape.

Mr. Paterson called AIG a “financially sound company,” as he announced that state regulators had agreed to grant it special permission to free up liquidity by borrowing up to $20 billion from its insurance subsidiaries.

He said his administration has been warning New Yorkers about the severity of the downturn, saying the situation would have been worse had he not called lawmakers back to Albany for an emergency budget-cutting session last month. “This is what we’ve been trying to underscore all year, or at least since March when I got here,” he said.

The governor, in an interview with an Albany television station, said: “It is entirely likely that you will be seeing legislators back in Albany before the elections.” In conversations with legislative leaders, however, Mr. Paterson did not raise the issue of an emergency session, legislative sources said.

Mr. Bloomberg said the city is in a strong position to weather a downturn because it has diversified its economy by investing in film, fashion, tourism, health care, higher education, and arts industries.

“Thanks to our fiscal prudence, we are better able to deal with this crisis,” he said. Last fall, the city imposed a temporary hiring freeze of municipal employees and ordered all city agencies to trim their budgets, measures that are saving the city more than $1 billion this fiscal year.

The mayor left open the possibility that he would try to enact the city’s first significant tax increase in more than six years. “We cannot balance the budget just by cutting more,” he said. “We can do more than we have and we will, and then we will just have to take a look at other ways of raising revenue.”

If he were to raise taxes, Mr. Bloomberg would most likely favor an increase in the property tax rate, a move that city lawmakers have opposed in the past. Before this weekend, the mayor had already warned that he might lift the rates before the end of the fiscal year.

After the September 11, 2001, terrorist attacks, Mr. Bloomberg raised property taxes by 18.5% to help plug a multibillion-dollar deficit. In 2007, he lowered the rate by 7% but said the reduction would only last as long as the city could afford it.

Comptroller William Thompson Jr. said that the city’s pension funds are “healthy.”

The banking turmoil will inflict the most damage to the finances of Albany, which relies more heavily on Wall Street as a source of revenue. In a healthy economy, Wall Street accounts for 20% of state revenues.

State officials said it was too early to gauge the magnitude of the fallout. Before the shakeout, Bear Stearns, Lehman Brothers, and Merrill Lynch were employing 30,000 people in New York, accounting for 10% of Wall Street wages and 15% of Wall Street bonuses. Lehman itself contributed roughly $100 million to state coffers each year in income taxes, according to one projection.

“The ramifications … will probably not full be appreciated for days, months, maybe even years,” Mr. Paterson said.

Already in the last year, New York has lost more than 11,000 jobs in the finance and insurance sectors. By the time the financial shakeout runs its course, the toll will be considerably higher, officials said, estimating that those industries could see layoffs of more than 40,000.

Experts estimate that one Wall Street job generally creates two or three others in the wider economy. Such a ripple effect means that more than 100,000 people could lose their jobs during this period of turbulence.

Mr. Bloomberg said he had spoken with the presidents of Merrill Lynch and Bank of America and that both had assured him that job losses would be minimal.

State officials started crunching third-quarter results yesterday and expected to come out with new revenue projections in a week.

Bracing for layoffs in the tens of thousands, the Paterson administration said it has mobilized teams of “rapid response specialists” from the Labor Department who are trained to help fired employees file unemployment claims, craft resumes, and sharpen interview skills.