The division highlights the challenge of setting monetary policy when Mr. Trump’s trade policy is clouding the outlook for an otherwise decent-looking economy. Because it is unclear how much trade tensions will slow growth and whether they will eventually ease, Fed policy must aim at a moving target as it tries to keep the economy expanding steadily.

The president’s next round of tariffs on Chinese goods is expected to take effect Sept. 1, and Mr. Trump has shown no sign of backing down, even as global growth shows cracks and after a powerful recession signal flashed in bond markets.

While consumer spending and overall economic growth are holding up in the United States, household confidence declined in preliminary August data as Americans became less positive about the economic outlook. Some businesses are holding off on investment as Mr. Trump’s trade war fuels uncertainty.

Given that backdrop, officials wanted to make sure they “avoided any appearance of following a preset course,” minutes from the meeting show. “Members generally agreed that it was important to maintain optionality” in setting interest rates.

Jerome H. Powell, the Fed chair, indicated at his news conference after the meeting that the Fed could make additional rate cuts, but did not commit to the timing or extent of future decreases. His comments, and in particular his characterization of the July move as part of a cyclical adjustment rather than the start of a series of cuts that will return borrowing costs to rock bottom, disappointed some investors.