The Federal Reserve said Monday it would adopt a tiered approach toward determining whether to grant financial institutions access to its payment systems and signaled that cryptocurrency companies would be subject to a higher level of review.

The Fed’s board in Washington issued final guidelines Monday for its 12 regional branches to use when evaluating applications for so-called master accounts with the central bank. Such accounts allow financial institutions—primarily banks—to move trillions of dollars a day on the Fed’s payment systems.

In recent years, financial-service firms that cater to cryptocurrency investors have sought master accounts from the Fed, saying access to the central bank’s payment systems would allow them to process orders from customers more efficiently. That has followed efforts by banking regulators in some states, such as Wyoming, to make it easier for such firms to obtain bank charters.

Under the tiered approach the Fed decided to adopt, applications from financial firms with state charters would face more scrutiny than applications from institutions insured by the Federal Deposit Insurance Corp. or subject to federal supervision.

“Institutions that engage in novel activities and for which authorities are still developing appropriate supervisory and regulatory frameworks would undergo a more extensive review,” the Fed said in a press release.

The guidelines reflect the skeptical view that officials inside the Fed and other regulatory agencies have taken toward the cryptocurrency market, which is largely unsupervised.

Fed Chairman Jerome Powell warned earlier this year that it was “easy to see the risks” in products such as cryptocurrencies. He said the asset class should be subject to the same rules as other financial products, calling regulation “necessary to level the playing, keep trust of users, [and] protect consumers.”

After proposing a clearer set of guidelines for granting access to its payment systems last year, the Fed received dozens of comment letters from cryptocurrency firms, bank lobbyists and consumer-protection groups.

Crypto companies such as Kraken, a trading platform that applied for a Fed master account in 2020 through its Wyoming-chartered affiliate, said uncertainty and prolonged delays in approving such applications could hinder financial innovation.

Write to Paul Kiernan at paul.kiernan@wsj.com