The recent slide in stocks has not persuaded Chicago Federal Reserve President Charles Evans that the central bank should stop raising interest rates.

In a CNBC interview Friday, Evans said the economy still looks strong and he and his fellow policymakers on the Federal Open Market Committee should continue to gradually normalize rates.

"After many, many years of accommodative policy, which I have supported strongly because inflation's now up at 2 percent, it's time to readjust the policy stance at least to neutral," he told CNBC's Steve Liesman during a "Squawk Box" interview. "Let's see how the economy is performing at that point and then we might have to do a little more after that."

Evans spoke at a delicate time for the Fed: President Donald Trump has ripped the central bank in recent days for raising interest rates as the economy continues to strengthen but market volatility rises. The Fed has pumped the target for its benchmark rate up to 2 percent to 2.25 percent, hiking six times since Trump has become president.

Like his fellow officials, Evans wouldn't be drawn into the controversy. He stressed that the Fed remains independent and is comfortable with the direction of monetary policy, though he conceded that "it's a fair question" of why rates are being pushed higher despite little threat from inflation.

"I can't answer that," when asked whether he thought it was appropriate for the president to openly criticize the Fed, "but I will say that the Federal Reserve, you know, has a large amount of autonomy that is granted us by Congress and the president."

"The natural adjustment of policy up a little bit above some benchmark that might be viewed as neutral I think is just what we do, and you know we let people comment," he said.

That question of what the Fed views as "neutral" — neither accommodative nor restrictive — has been critical for markets as of late.

Fed Chairman Jerome Powell helped ignite the recent sell-off by saying Oct. 3 that the Fed is "a long way" from neutral. The comment sparked worries that the central bank would continue hiking rates beyond what the market expects, and Evans' interview Friday did little to dispel the notion that Fed officials are willing to go beyond the neutral rate as unemployment continues to fall.

Fed officials worry that waiting too long to increase rates could cause financial imbalances like those that have led to previous bubbles and subsequent economic downturns.

"I would say that with the unemployment rate headed to three and a half percent, we're in a more normal environment where an accommodative stance of policy, when we've got pro-cyclical fiscal policy and a very strong economy, we probably need to be a little bit on the above-neutral side, but I don't know that we need to be a lot," Evans said.

"At the moment [the economy] looks really good," he said. "Fundamentals are strong."