The Federal Reserve approved a final rule Wednesday that brings the government closer to placing large nonbank companies that were at the heart of the financial crisis under stricter supervision.

The rule leaves a strikingly wide swath of companies on the table as potentially falling under tougher oversight, including private-equity firms and hedge funds. Yet industry officials and others following the process say it’s unlikely that officials will ultimately single out more than a handful of firms.

Jaret Seiberg, a managing director at Guggenheim Securities, said in a report Wednesday that the most likely firms to be designated are GE Capital, American International Group, Prudential and MetLife.

Any final decision by officials will be closely watched by Wall Street, since a company designated by the government as “systemically important” would face tougher capital standards, among other restrictions, that could eat into the firm’s profitability.

“The Fed has taken a very broad view of the types of activities covered in the definition, which gives [regulators] a good deal of discretion,” said Karen Shaw Petrou, managing partner of Federal Financial Analytics, a consulting firm.

It has taken federal regulators nearly three years since the passage of Dodd-Frank, the country’s overhaul of Wall Street rules, to define which nonbank companies, if they were to fail, could threaten the integrity of the country’s financial system.

“If you can’t designate someone like GE Capital or AIG, which helped trigger the financial crisis, after three years, how are you going to keep up with how quickly the financial system changes?” said Marcus Stanley, policy director at Americans for Financial Reform, a watchdog group. “If this is going to be our response time to things, that’s not so good.”

Wednesday’s move indicates that the Financial Stability Oversight Council, an interagency panel of regulators, is in the final stages of reviewing institutions. Regulators say they will vote in the next few months on which companies will fall under increased scrutiny.

Under the language of the Fed’s final ruling, large private-equity firms and hedge funds could technically be ruled as nonbanks, qualifying them for greater scrutiny. But those familiar with the process say that is unlikely, given that the firms played no major role in causing the crisis.

To be considered a “systemically important” nonbank, a firm must derive at least 85 percent of its revenue or assets from financial activities. The rule from the Federal Reserve also lays out exactly what qualifies as financial activity.

To determine which firms should be subject to additional oversight, regulators initiated a three-step process. First, they examined all nonbank firms with more than $50 billion in assets. They then whittled down the list to firms that met other criteria, such as having high leverage ratios or holding more than $20 billion in debt.