MetLife, the nation’s largest life insurance company, said Tuesday that financial regulators have moved one step closer to placing it under tougher government supervision.

In a closed session on Tuesday, the Financial Stability Oversight Council voted to advance MetLife to the final stage of a three-step process for designation as a systemically important financial institution (SIFI), a label that would subject the firm to oversight from the Federal Reserve. That would impose on the company a number of strict regulations, including setting aside more money to cushion against losses.

For months, MetLife’s chief executive Steve Kandarian has warned that the FSOC’s plans to subject insurance companies to federal oversight could lead to higher prices and fewer products across the industry. He stressed that point Tuesday, suggesting MetLife could dial back its business in the face of higher capital requirements.

“If only a handful of large life insurers are named SIFIs and subjected to capital rules designed for banks, our ability to issue guarantees would be constrained,” he said in a statement. “We would have to raise the price of the products we offer, reduce the amount of risk we take on, or stop offering certain products altogether.”

Kandarian said he anticipated the council would name MetLife because the company is larger than its competitor Prudential Financial, which is appealing the government’s designation.

It’s unclear what action MetLife would take if it meets Prudential’s fate, since the company declined to comment on the matter. But Kandarian is unwavering in his belief that Metlife does not engage in the sorts of risky financial activities that could rattle the economy.

“Not only does exposure to MetLife not threaten the financial system, but I cannot think of a single firm that would be threatened by its exposure to MetLife,” Kandarian said in the statement.

Tuesday’s vote arrives a week after the council finalized its designation of GE Capital and American International Group. The interagency panel of regulators has ushered in a new era of oversight for a broad swath of firms that play in the financial markets but have largely escaped federal supervision, including private equity firms and hedge funds.

The goal of the designations is to ensure that nonbank financial firms will not fall through the cracks of the regulatory system the way AIG did at the start of the financial crisis. Lawmakers called for tougher oversight of financial companies after the insurance giant received a $182 billion bailout to save it from collapse in 2008.

In a memo explaining the AIG decision, regulators said the company could face the equivalent of a bank run if policyholders got spooked about its financial health and cashed out en masse. The same could be said for MetLife or Prudential.

Kandarian argued in his statement that the council’s scenario is a little far fetched because “even during periods of financial stress, the long-term nature of our liabilities insulates us against bank-like ‘runs’ and the need to sell off assets.”

MetLife’s main rival Prudential has requested a closed-door hearing before the FSOC, which has until August to schedule the meeting. Attorneys and others following the process doubt that Prudential has much of a chance of getting the FSOC to reverse course.

The three-step process of examination was so lengthy and detailed that it may be difficult for Prudential to make its case at this point, analysts say. Any outcome could have significant bearing on how regulators proceed with future designations.