A tentative sense of relief prevailed among investors on Friday morning following two very different financial rescues the day before: one of a global banking giant in Switzerland and another of a midsize regional lender in San Francisco. The moves to shore up the flailing lenders with injections worth tens of billions of dollars had produced a pause in the mayhem that had gripped banks and markets.

As Asia and Europe opened for business on the last day of a tumultuous week, markets conveyed a measure of calm, at least for the moment. Stock indexes in Asia and Europe posted gains, and banks recovered some of their losses.

“We’re starting to see a modest change in the mood music,” Jim Reid of Deutsche Bank wrote in a Friday note assessing the early moves in markets, citing the stabilization of bank stocks and signs of less stress in the bond market, after the European Central Bank on Thursday stuck to its plan to raise interest rates despite the market turmoil.

Still, there is little confidence that this crisis has fully run its course. Banks in the United States borrowed record amounts from the Federal Reserve to meet short-term needs this week, and shares of the recently rescued banks remain shaky.

Some sense of solace took shape just after midnight on Thursday in Zurich, when Credit Suisse, facing questions about its financial health, announced that it had grabbed a $54 billion lifeline from Switzerland’s central bank. Credit Suisse has been battered by years of mistakes and controversies that have cost it two chief executives over three years. But on Thursday, shares in the 166-year-old Swiss bank, which had plunged to a record low the day before, turned around and rose nearly 20 percent.

The rescue of Credit Suisse, which the bank and Swiss regulators had insisted needed no rescue, followed a classic playbook: A powerful central bank threw its full support — and a big chunk of financial firepower — behind an institution that investors had decided needed urgent help. Investors responded in kind.

Later that day, First Republic Bank, a midsize lender based in San Francisco whose stock price has fallen more than 70 percent this month, erasing roughly $16 billion in value, announced a $30 billion rescue package that was as unconventional as the Credit Suisse support was traditional.

Four storied names in American finance — JPMorgan Chase, Bank of America, Citigroup and Wells Fargo — agreed to each place $5 billion in uninsured deposits with First Republic. Goldman Sachs and Morgan Stanley, mainstays of Wall Street, pitched in $2.5 billion apiece, and five smaller regional banks added $1 billion each.

The industry-led action spoke loudly: These 11 institutions were confident that First Republic deserved saving. The banks, normally fierce rivals, issued a joint statement explaining their move: “America’s larger banks stand united with all banks to support our economy and all of those around us.”

The government’s overseers of the banking industry, some of whom helped bring the deal together, stood on the sidelines, issuing a bland statement saying that the banks’ show of support for First Republic was “most welcome.”

Stocks in the United States on Thursday swung from early losses to close 1.8 percent higher. The S&P 500 index remains up for the year and is on course to close out its second-best week of 2023, absent another reversal on Friday. U.S. stock futures, which signal the direction markets will take when they open in New York, indicated a flat open on Friday, retaining Thursday’s gain.

Signs of anxiety persist. New data from the Federal Reserve released on Thursday also showed that banks borrowed record amounts of emergency funds from the central bank, tapping both existing facilities and a new program to shore up liquidity that was announced after the government takeovers of a once-obscure lender to the tech world, Silicon Valley Bank, and the small Signature Bank in New York. That said, the borrowing was still smaller, as a share of the banking system’s current deposit base, than it was during the last surge of emergency borrowing, during the financial crisis of 2008.

And Credit Suisse’s shares are slipping again, eroding some of Thursday’s gains. The same goes for First Republic, with premarket losses on Friday erasing part of the previous day’s gain, suggesting that trading in banking shares will remain volatile on Friday.

Analysts at UBS wrote that banking stocks would “truly settle only after the market feels as if there is a longer-term solution” to First Republic’s woes. An index tracking the largest U.S. largest banks has fallen nearly 20 percent this year, with much of the loss concentrated in the past week, lagging the gain in the broader market over that period.

Before the broad panic about banks first surfaced last week, the biggest challenge facing economic policymakers was rapid inflation. Central bankers were caught between trying to tame price rises while not causing growth to stall out. Those efforts suddenly appeared far more complex with the sudden prospect of successive bank runs.

With a few exceptions, bank stocks, the focus of this week’s turmoil, appeared to regain their feet at the end of a seesaw week of trading. But “we shouldn’t get ahead of ourselves,” Mr. Reid of Deutsche Bank said. “It’s worth remembering that we’ve already had a temporary period of stability on Tuesday that was then dented by the Credit Suisse worries on Wednesday.”

Joe Rennison, Rob Copeland and Lauren Hirsch contributed reporting.