Thomas W. Davis, a vice chairman who had overseen investment banking and sales and trading of stocks and bonds, quit this fall.
In that position, Mr. Fuld will oversee trading at the firm.
The Big Board and the Amex are auction markets, in which all orders come together on a trading floor, with one specialist overseeing trading in each stock.
Regulators from each country would continue overseeing trading in those countries.
But the board of the National Association of Securities Dealers, which oversees over-the-counter trading, has voted to oppose the plan.
Mr. Fisher, who oversaw sales and trading, had been considered the heir apparent.
In his new post, he will continue to oversee fixed-income trading and add equities, a business that is trailing bonds in profitability.
"We've been in bear markets before," said Brian Zipp, who oversees mortgage-backed trading at Lehman Brothers.
The N.A.S.D. is the self-regulatory organization for the over-the-counter market and oversees electronic trading on the Nasdaq system.
The specialists oversee trading.