San Francisco Fed President Mary Daly said Wednesday that the strength of the economy and still-high readings on inflation suggest the Federal Reserve needs to raise interest rates further, but how much more will depend on how much credit tightens as a result of recent bank failures.

In her first comments since the failure of Silicon Valley Bank, which is overseen by the San Francisco Fed, Daly said that the "full impact of this policy tightening is still making its way through the system."

"The strength of the economy and the elevated readings on inflation suggest that there is more work to do," she added. "How much more depends on several factors, all with considerable uncertainty attached to their evolution."

One of those factors, according to Daly, is any lingering reverberations from the failures of Silicon Valley Bank and Signature Bank, which could force banks to pull back on lending. Daly says credit standards have risen over the past year and are expected to increase further in coming quarters and that recent data on lending already point to declines in lending volumes in several sectors.

"History tells us that as banks evaluate the changing economic outlook and manage their liquidity and balance sheets, they are likely to tighten credit availability," Daly said. "How much credit tightening will ultimately occur is not yet known."

Daly is also watching the global economy and how it could impact U.S. growth, noting that central banks around the world that are raising interest rates to bring down inflation as well as tighter international bank conditions could cause the global economy to slow and serve as a headwind for U.S. growth.

“There are good reasons to think that policy may have to tighten more to bring inflation down,” Daly said. “But there are also good reasons to think that the economy may continue to slow, even without additional policy adjustments.”

Daly’s comments come as the consumer price index for March showed that headline inflation continued to cool. However, the report showed the core prices, which exclude volatile energy and food prices and to which the Fed pays closer attention, increased by 5.6%, accelerating slightly from 5.5% the prior month.

"We had some good news today on the CPI," Daly said of the report. "Headline release showed that it's going down, it's going in the right direction, but it's still elevated. It's not consistent with price stability. And I'm going to be looking specifically in the CPI and in our other measures to see if core services are coming down and really core services minus housing."

Daly says the job market still remains very strong, underscoring that the economy has added close to 350,000 jobs per month over the first three months of this year, compared with the 90,000 jobs needed each month to keep up with the growth of the labor force.

“There are a number of signs that the labor market is starting to cool, but it remains extremely tight and is likely to come back into balance only gradually,” Daly said.