Delaying some of the tariffs, however, may actually have taken pressure off the Fed to act by increasing the chances that China and the United States will reach some sort of a deal before the full set of penalties take effect. In fact, while Wall Street forecasts had begun to point to a half-percentage-point rate cut in September, expectations of just a quarter-point cut increased after the tariff delay was announced.

Fed policy was not crucial to the decision to delay tariffs — that centered on consumers and the economy, according to people familiar with the deliberations — but the report that it is on advisers’ minds is noteworthy. It suggests that for at least some White House advisers, one consideration in shaping and selling trade policy is keeping the central bank pointed toward interest-rate cuts.

The Fed cut rates in July for the first time in more than a decade, partly in response to mounting risks from the trade war and a global economic slowdown. It signaled that it might make further cuts if global risks persisted and inflation stayed low.

Administration economists have continued to predict, as recently as July, that the economy will grow at a 3.2 percent rate this year, up from 2.5 percent last year. (Officials will complete a revised forecast at the end of October.) But if economic growth continues at its current pace through the fall, Mr. Trump will need a rapid acceleration — to more than 5 percent growth in the fourth quarter — to hit his administration’s initial target for this year.

On Wednesday, Mr. Trump wrote on Twitter: “China is not our problem, though Hong Kong is not helping. Our problem is with the Fed. Raised too much & too fast.”

But the main threat to United States growth, most economists say, is slowing economic expansion abroad and the possibility that Mr. Trump’s trade war will intensify the global pullback and chill investment and expansion domestically.

“I don’t know if he’s necessarily doing this just to get the Fed to cut,” said Gennadiy Goldberg, senior United States rates strategist at TD Securities, but the trade war “puts the Fed between a rock and a hard place,” because it wants to avoid playing into politics but must also protect the economy.