The economy is on track to later this year satisfy the Federal Reserve’s threshold to begin reducing its $120 billion in monthly asset purchases, a top central bank official said Tuesday.

Chicago Fed President Charles Evans said he expected recent employment gains to continue, which would allow the Fed to declare that the economy has achieved the “substantial further progress” it laid out last December.

“I’d like to see a few more employment reports” before making that determination, Mr. Evans told reporters during an online news conference. “We’re coming upon a time where it’s definitely going to be appropriate to start” reducing the pace of asset purchases.

“There’s a sense in which you want to be careful that you don’t start prematurely [and] you don’t start too late,” said Mr. Evans, who is a voting member of the rate-setting Federal Open Market Committee this year.

Mr. Evans said he expects the unemployment rate to fall to 4.5% by year’s end and the Fed’s preferred inflation gauge, excluding volatile food and energy categories, to end the year around or slightly above 3%. That gauge hit 3.5% in June, its highest level in three decades amid supply-chain bottlenecks associated with reopening the economy.

Mr. Evans said he expects that core inflation gauge to decline to around 2.1% by the end of next year. He said he hoped the central bank would remain on guard against prematurely declaring that it had achieved its inflation objective. Last year, the Fed said that it wanted inflation to average 2% over time and that it would seek inflation that is moderately above 2% for some time to make up for periods in which inflation ran somewhat below the target.

“I’m going to be very regretful if we sort of claim victory on averaging 2% and then we find ourselves in 2023 with about a 1.8% inflation rate, sustainable, going forward. That would be a challenge for our long-run framework,” he said. “We ought to be willing to average inflation above 2%—frankly, well above 2%.”

But Mr. Evans conceded that there is significant uncertainty around the path of inflation. “I don’t have strong confidence in what the sustainable inflation data are going to look like next year,” he said.

Write to Nick Timiraos at nick.timiraos@wsj.com