While "no one knows for sure" if there is a big problem lurking in the financial sector right now, "so far, we haven't seen the kind of market dysfunction, even through what's happening in the global markets right now, we haven't seen that in the U.S. markets," Mester said in an interview on CNBC.

Mester touched on market conditions amid very unsettled conditions across the globe. She acknowledged that Bank of England actions this week to buy bonds to stabilize markets there appeared at odds with its work to lower inflation.

The BoE's actions appeared "a little bit incoherent because they were buying bonds at the same time they're talking about raising interest rates," Mester said. But she added there were "good reasons" for what the UK central bank did, saying "market functioning is incredibly important, because you won't be able to hit any monetary policy goals if the markets aren't functioning."

Mester, who holds a voting role on the rate setting Federal Open Market Committee, said she still sees inflation as the paramount problem facing the economy, which means the central bank needs to press forward with rate rises, lifting a federal funds target rate range now at between 3.00%-3.25% to over 4%.

The Fed has faced concerns that its aggressive rate hikes aimed at lowering inflation from 40-year highs will send the economy into recession. Financial markets have also been under broad pressure and suffered steep losses, and many observers worry Fed actions, coupled with rate rises from other major central banks, could trigger market dysfunction.

Mester said she does not see a case for slowing down on rate rises right now. She noted that at last week's FOMC meeting officials penciled in a path for the federal funds target rate that will get it to 4.6% next year and said she expects the central bank will likely have to go further than that.

"I probably am a little bit above that median path because I see more persistence in the inflation process," Mester said. Getting above a 4% fed funds rate is important to helping to lower inflation, she said.

Mester also said job market demand continues to outpace supply. She also said the strong dollar is a helpful force to lower U.S. inflation.

(Reporting by Michael S. Derby; Editing by Dan Burns and Chizu Nomiyama)

By Michael S. Derby