(Reuters) -Federal Reserve Bank of Atlanta President Raphael Bostic said Tuesday inflation risks are still in play in the U.S. economy, although he noted that thus far President Donald Trump's import tax hikes have not pushed up prices the way they were expected to. 

"Business leaders are telling us they are definitely feeling the cost pressures and it is becoming increasingly difficult to prevent those from flowing into prices that are faced by consumers and by their customers," Bostic said during a live taping of the Macro Musings podcast.

When it comes to inflation, "I actually think there's still more to come" on that front.

While the president's tariffs are one of the main upward pressures on inflation right now, Bostic said when it came to how much the tariffs had pushed up prices, "it's been much more muted, I think, than many expected."

Bostic said it was now important for the central bank to keep a close eye on how high inflation was affecting expectations about the future of prices. 

With inflation, "I really think we need to pay very close attention to the consumer psyche and to what businesses plan" given the current environment, he said.

Bostic did not comment directly on the monetary policy outlook, following last week's meeting that saw officials cut their overnight interest rate target range by a quarter percentage point, to between 4% and 4.25%. Driving the rate cut was a concern that labor markets are stalling and would benefit from lower short-term borrowing costs. 

In his appearance, Bostic noted "the labor markets are very difficult to interpret today," and that businesses were telling him that amid the uncertainty, they were neither hiring nor firing to a notable degree.