If the Federal Reserve doesn't raise interest rates in December, it could cause turmoil the stock market, former Wells Fargo CEO Dick Kovacevich told CNBC on Thursday.

The central bank has recently come under attack by President Donald Trump, who has repeatedly criticized its decision to raise interest rates.

Kovacevich said the Fed "has" to hike rates because it has telegraphed it will do so.

If it doesn't, the markets will plunge because it will seem like the Fed "caved to the president," he said.

"The independence of the Federal Reserve is instrumental to any market economy. If that ever comes into question, the market is going to react very negatively," Kovacevich said on "Power Lunch."

While it is unusual for presidents to openly criticize the Fed, Trump has done just that.

Among other things, he said the Fed has "gone crazy" by continuing to raise rates and has called the central bank his "biggest threat." He also blamed Fed Chair Jerome Powell for last month's market correction and said he wasn't happy with Powell's "loco" decision to move forward with rate increases.

However, Trump is making a miscalculation, Kovacevich suggested.

"What he doesn't understand is that the more he tries to influence the Fed by public statements, the less likely he is to influence the Fed, because the Fed has to remain and be perceived as being independent," he said.

On Thursday, the Federal Open Market Committee voted to keep its federal funds rate in a range of 2 percent to 2.25 percent. In addition to the expected December rate hike, officials at the September meeting pointed to three increases next year.

Kovacevich believes the Fed is doing a great job and has been very transparent.

"Because we have a very strong economy, we have very low unemployment, we have reasonably low inflation … the Fed does not need to continue to be accommodative," he said.

Instead, the central bank has to get to a neutral rate, which Kovacevich thinks is between 3 percent and 3.5 percent, although he noted that could change.

— CNBC's Lori Ann Larocco and Jeff Cox contributed to this report.

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