Chicago Fed President Charles Evans said in a speech on Tuesday that the Fed should delay its interest rate hike until there are signs that inflation is accelerating toward 2% target.

"Before raising rates, I would prefer to have more confidence than I do today that inflation is indeed beginning to head higher. Given the current low level of core inflation, some evidence of true upward momentum in actual inflation would bolster my confidence," he said.

Evans noted that the Fed should hike its interest rates gradually once it starts raising its interest rate.

"To me, it is vital that when we first raise rates, the FOMC also strongly and effectively communicates its plan for a gradual path for future rate increases," Chicago Fed president said.

He thinks that the interest rate should be "under 1 percent at the end of 2016", and he expects the U.S. economy to expand about 2.5% in 2016.

Evans is a voting member of the FOMC this year.