Richard Drew/Associated Press

Morgan Stanley will slash 580 jobs in New York as part of a broader wave of layoffs underway at the bank, according to a public filing.

In a notice filed with the New York State Department of Labor, Morgan Stanley cited “economic” woes as the cause of the layoffs. The cuts began Dec. 15 on a “rolling” basis, according to the filing, known as a WARN, or Worker Adjustment and Retraining Notification.

Earlier this month, Morgan Stanley said it would cut 1,600 jobs, or 2.6 percent of its work force, by the first quarter of 2012. The bank plans to spread the round of reductions across all divisions, including investment banking and trading.

The layoffs at Morgan Stanley are the latest round of severe cutbacks on Wall Street, which has suffered a year of humbling returns and enormous cost-cutting. Citigroup recently announced it would shed 4,500 jobs. Bank of America and Goldman Sachs have also begun carrying out major staff reductions. In June, Goldman told the New York Department of Labor that it would layoff 230 New York workers through March 2012.

The job losses have taken a toll on New York City, the center of the financial industry. The securities industry in the city lost nearly $3 billion in the third quarter, according to a report released this month by the New York State comptroller. In October, the comptroller disclosed that an estimated 10,000 Wall Street workers could lose their jobs by the end of 2012.

Some of the cuts at Morgan Stanley in New York, the filing said, will impact workers at the firm’s Midtown Manhattan headquarters, 1585 Broadway. The layoffs will also affect three smaller Morgan Stanley offices in New York: 1 New York Plaza, 750 Seventh Avenue and 1221 Avenue of Americas.