WASHINGTON, May 6 (Reuters) - The U.S.-backed war against Iran is looking increasingly like an inflationary shock to the economy, with little apparent impact yet on jobs and growth but concerns rising about tangled supply chains and more persistent price increases, Chicago Federal Reserve President Austan Goolsbee said on Wednesday.

"It has not yet been a stagflationary-direction shock," with a blow to both the job market and inflation that would force the U.S. central bank to decide which of its goals is more at risk, Goolsbee said on a video call with journalists after participating in a Milken Institute conference in Los Angeles. "It has just been an inflationary shock. And the longer that continues, the more nervous that makes me."