WASHINGTON—The potential for U.S. public health to worsen as the Covid-19 pandemic continues is one of the greatest near-term risks to the financial system, the Federal Reserve said, while noting that asset prices are susceptible to large declines should investor sentiment shift.

Any deterioration in the public-health situation could slow the recent economic recovery, particularly if widespread business closures returned and supply chains were further disrupted, the Fed said. The number of new Covid-19 cases has fallen in...

WASHINGTON—The potential for U.S. public health to worsen as the Covid-19 pandemic continues is one of the greatest near-term risks to the financial system, the Federal Reserve said, while noting that asset prices are susceptible to large declines should investor sentiment shift.

Any deterioration in the public-health situation could slow the recent economic recovery, particularly if widespread business closures returned and supply chains were further disrupted, the Fed said. The number of new Covid-19 cases has fallen in recent months, but a resurgence this summer, tied to the Delta variant, coincided with a slowdown in hiring and economic growth.

“Asset prices may be vulnerable to significant declines should risk appetite fall, progress on containing the virus disappoint, or the recovery stall,” the central bank said in its semiannual Financial Stability Report.

Still, other parts of the financial system appear resilient. Banks remain well capitalized, the central bank said, and key measures of vulnerability from business and household debt have largely returned to pre-pandemic levels.

“Little evidence exists of widespread erosion in mortgage underwriting standards or speculative practices,” the report said. “However, with valuations at high levels, house prices could be particularly sensitive to shocks.”

The Fed also warned that structural vulnerabilities persist in some types of money-market mutual funds and other cash-management vehicles, as well as in bond and bank loan mutual funds. The vulnerabilities could amplify shocks to the financial system in times of stress, as they have in prior crises, the central bank said.

Fed officials monitor asset prices to gauge risks that a sudden, sharp decline might pose to the broader financial system. The way in which they characterize financial stability risks has implications for whether they decide to activate the so-called countercyclical capital buffer—a tool that would require banks to hold more capital should the economy show signs of overheating. They have never turned the buffer on.

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In the financial crisis of 2007-2009, the collapse of residential property values caused overextended homeowners to default on their mortgages, inflicting losses on banks and other financial firms, driving share prices lower and leading to the longest recession since the 1930s.

Last year’s downturn early in the Covid-19 pandemic was different. The longest economic expansion on record had put the average American household in relatively strong financial shape, and banks were well-capitalized as a result of regulations enacted after the 2008 crisis. As economic activity collapsed in March 2020, the government used its borrowing capacity to step in with trillions of dollars in aid to households and businesses.

Still, Fed officials have indicated that they continue to have serious concerns about risks in asset markets. Staff at a July Fed meeting characterized vulnerabilities to the financial system as notable, pointing in part to rapidly increasing house prices that had left valuation measures stretched.

Write to Andrew Ackerman at andrew.ackerman@wsj.com