"I agree with the president on the economics," he said during an interview on CNBC's " Squawk Box ." "I think maybe not the 100 basis points [cut] that he mentioned yesterday, but in general I think the Fed has been too tight."

While he expressed some reservations about the impact a sitting president's criticism could have on Fed independence, Kocherlakota said the notion that monetary policy is too restrictive is basically correct.

The comments come a day after Trump's latest broadside against the U.S. central bank in which he contended that a rate cut of 100 basis points, or 1 percentage point, should happen "over a fairly short period of time."

In a pair of tweets on the issue, Trump accused Fed Chairman Jerome Powell and his colleagues of showing a "horrendous lack of vision."

Kocherlakota served on the Fed from 2009 to 2015 and was considered one of the institution's leading dovish voices, meaning he favored lower interest rates. Just as he was leaving his post, the policymaking Federal Open Market Committee approved its first rate hike in a decade after keeping its benchmark overnight funds rate near zero for seven years.

After that initial hike, the committee raised rates eight more times before cutting in July. In the past, few if any presidents have been as publicly vocal in their criticism of Fed policy as Trump, who has said the economy would be doing much better if not for the rate hikes.

"I think the president's role ... is not to be as out there criticizing the Fed," Kocherlakota said. "I think that can lead to doubts about the Fed's credibility going forward. It's not much of a problem now."

He cited low inflation as a primary reason why the Fed should be cutting here. The committee considers 2% a healthy level, and the economy has not been able to sustain that during the decade-long recovery.

While Kocherlakota conceded that cutting might not allow for much maneuverability during the next downturn, he said it's important to keep rates low if a downturn is on the horizon.

"When a recession shock comes along, we really want to have a much lower interest rate," he said. "If we raised interest rates now, we'd just be choking off the economy."