The concern over trade was evident at Mr. Powell’s appearance before the Economic Club of Chicago. The Fed chief did not mention tariffs in his speech, but in a question-and-answer session afterward, they were the first topic raised.

The Fed chief, who took his post in February, said it was “too early to say” what impact the dueling trade measures would have. “We don’t know the extent to which the tariffs will actually come into effect and, if so, how big will that effect be and what will the timing of it be,” Mr. Powell said. But he made it clear that the Fed would watch closely for any sign that the trade dispute was knocking the recovery off course.

The trade tensions complicate what was already a tricky task for the Fed. Hundreds of billions of dollars in tax cuts and spending increases risk fueling inflation, as do wage pressures from a robust labor market. The government’s monthly jobs report on Friday, while more subdued than in recent months, still pointed to a healthy employment picture.

Yet policymakers are wary of acting too aggressively to slow the economy at a time when wage growth has been tepid. The Fed’s response has been gradual interest-rate increases.

A trade war could act as a drag on economic growth, forcing the Fed to be even more cautious. But tariffs could also raise consumer prices by limiting cheap imports from China and other countries. That could increase the risk that the Fed will lift rates too quickly, choking off the recovery.