"While Trump’s comments on how he was 'not thrilled' by the Federal Reserve’s interest rate rises could create a sense of uncertainty over Washington’s Dollar policy, it is unlikely to derail the Fed from gradually raising interest rates," Lukman Otunuga, research analyst at forex brokerage FXTM, said in a note.

Market participants still expect the Fed to hike twice more this year, with the probability for increases in September and December changing little after comments from Trump in a CNBC interview and on his Twitter feed .

While making for more eye-popping headlines out of the Oval Office, the president's complaints that rising interest rates are hampering economic progress did not move the fed funds futures market, where traders make bets about the Fed's future moves.

President Donald Trump 's criticism of monetary policy won't have much impact on how the Federal Reserve goes about its business, judging by initial market reaction.

Indeed, the CME Group's FedWatch tracker indicated on Friday a 91 percent chance of a September move and a 61 percent probability of another hike in December. In fact, the December reading actually was about 2 percentage points higher than on Thursday before Trump lamented rising rates in a CNBC interview.

Trump amped up his Fed criticism Friday, but markets still weren't expecting central bank officials to take the remarks to heart.

"Trump’s verbal intervention is likely to hit a brick wall, as heightened rate hike expectations ensure that the Dollar reigns supreme across currency markets," Otunuga said.

"I don’t think the market will react too much. This is typical stream of consciousness Trump with an unfortunate comment," added David Nelson, chief strategist at Belpointe. "We’re getting used to it now."

Still, there continued to be worries that Trump's railing about Fed Chairman Jerome Powell and his fellow policy setters could compromise the central bank's independence. Most presidents have steered clear of commenting on monetary policy on the belief that the Fed should set rates based on what's best for the economy free of political concerns.

"So somebody would say, ‘Oh, maybe you shouldn’t say that as president.' I couldn’t care less what they say, because my views haven’t changed," Trump told CNBC, after calling Powell "a good man."

Those kinds of comments will have market pros watching how Fed policy unfolds.

"We understand that Fed policy is run by a committee, but the focus will be on Powell, and we worry that he can't win; regardless of what he does, his motives will now be questioned," Greg Valliere, chief global strategist at Horizon Investments, said in his daily note. "Anti-Powell tweets from Trump are likely by year-end, an irritant the markets could do without."

Similar sentiment was expressed elsewhere.

Craig Erlam, senior market analyst at forex traders Oanda, worried that pressure from Trump "could be a major risk for the economy" if it knocks the Fed off its gradual tightening path.

"Ultimately, I don’t expect the Fed to be influenced but that doesn’t mean Trump won’t find an alternative way to deal with the issues, even if such solutions are controversial and prove ineffective or self-defeating," Erlam said.

And Fawad Razaqzada, market analyst at Forex.com, said Trump is making himself look like "a bit of a hypocrite" because it is the president's pro-growth policies, including tax cuts and spending increases, that have helped push the Fed into its tightening stance.

"He was the one who cut taxes and promised or delivered big spending aimed at creating jobs and raising incomes. What’s more, protectionist policies are raising import costs, leading to higher inflation," Razaqzada said. "It is the Fed’s mandate to control inflation and the only way to do that is by tightening monetary policy. You can't have your cake and eat it."

— CNBC's Tae Kim contributed to this report.