Markets have rallied after a group of US banking giants stepped in to rescue a smaller regional lender, which had been seen as at risk of failure.
Investors’ worries over a crisis in the banking sector were eased after 11 US banks injected $30bn (£24.8bn) into First Republic.
Recent bank collapses in the US have raised fears over the health of the banking system.
Japan’s Nikkei share index closed higher, helped by rising bank shares.
European shares are also expected to open up when trading begins.
The 11 US banks who announced the support said the action reflected their “confidence in the country’s banking system”.
US financial officials said: “This show of support by a group of large banks is most welcome, and demonstrates the resilience of the banking system.”
After the failure of two US banks in the past week – Silicon Valley Bank (SVB) and Signature Bank – investors have been worried that other banks could also be about to collapse.
US regulators stepped in at the weekend to ensure that customers at SVB and Signature Bank had full access to their money.
Shares in San Francisco-based First Republic had sunk nearly 70% over the last week, amid fears it would be the next bank at risk of a rush of customers withdrawing their deposits.
But the rescue plan by the 11 banks, led by JP Morgan and Citigroup, boosted stock markets, and shares in First Republic were up more than 20% at one point.
However, there are signs that not all worries have been eased.
Shares in First Republic dropped 20% in after-hours stock market trading after the bank said its was suspending its dividend – its payment to shareholders – “during this period of uncertainty”.
Swetha Ramachandran, investment director at GAM Investments, said authorities were moving “proactively” to stop the problems spreading throughout the banking sector.
“What they’re trying to do is really ringfence the specific issues around individual isolated banks to stop them from becoming systemic,” she told the BBC’s Today programme.
“So this is very different to 2008 which was a widespread issue across the banking sector.”
On Thursday, US Treasury Secretary Janet Yellen said “the banking system overall is safe and sound”, while the vice president of the European Central Bank (ECB), Luis de Guindos, said Europe banking sector was “resilient”.
Europe has not escaped the jitters in the banking sector, due to difficulties at Swiss bank giant Credit Suisse.
Shares in Credit Suisse sank earlier in the week on concerns over its future, before the Swiss National Bank said on Wednesday that it was supplying the bank with up to £44bn in emergency funds.
Central banks around the world have sharply raised borrowing costs over the past year to try to curb the pace of overall price rises, or inflation.
The moves have hurt the values of the large portfolios of bonds bought by banks when rates were lower, a change that contributed to the collapse of Silicon Valley Bank, and has raised questions about whether other firms are facing similar situation.
Jeffrey Cleveland, chief economist at US asset manager Payden and Regal, said there was the potential for other banks to be caught up in the problem.
“There could be other vulnerabilities… if central banks are intent on continuing to raise interest rates,” he told the BBC’s Today programme.
“Historically when that happens we do see fragility, we do see problems in the financial system. It wouldn’t surprise me at all if other vulnerabilities do appear.”
On Thursday, the ECB announced a further increase to interest rates from 2.5% to 3%.
“For the ECB their core fight right now is against inflation,” said GAM Investments’ Ms Ramachandran.
“While they’re monitoring wider financial market stability I think their view was that the Credit Suisse issues are idiosyncratic and contained to that specific bank.”