Investing.com -- Chicago Federal Reserve Bank President Austan Goolsbee said Tuesday he is concerned the Iran war will drive inflation higher while slowing the economy, creating a challenging situation for the central bank with no clear policy response.

"My concern at this immediate time is that we've got to get our heads around an oil shock which is going to drive up prices in a stagflationary way," Goolsbee said in Detroit. "The prices spiked from tariffs and they were supposed to go away, and this is now hitting before that went away."

Goolsbee described the current environment as uncomfortable, noting there is no obvious cookbook for the Fed to follow. He said rising oil prices represent a stagflationary shock, with $5 per gallon gasoline expected to affect the supply chain.

The Fed official said the job market remains stable but not great, adding he is cautious and nervous about the economy. He warned that prolonged high inflation risks becoming ingrained in the economy, though he expressed hope the impact from oil will prove temporary.

Goolsbee emphasized the Fed's independence, stating nothing in the Federal Reserve Act requires making the stock market or the president happy. He said actively discussing removal of Fed independence would be a bad idea, warning inflation would come roaring back.

The Fed official noted there is anxiety about inflation returning to the economy.