President Trump’s relentless attacks on the Federal Reserve and its chair, Jerome H. Powell, have put the central bank under intense scrutiny as it grapples with when and by how much to cut interest rates again after a long pause.

Officials at the Fed are set to gather for their next meeting on monetary policy in less than two weeks, and they are expected to keep interest rates steady for the fifth time this year as they wait to see the impact of Mr. Trump’s tariffs and other policies on the economy.

That decision has been highly telegraphed. But it comes at a moment of acute tension between the White House and the Fed. Mr. Trump, angered by the central bank’s reluctance to lower borrowing costs, has stepped up his pressure campaign on Mr. Powell, repeatedly insulting him and even going so far as to brandish a draft letter firing him to House Republicans in the Oval Office this week.

“The USA is Rockin’, there is VERY LOW INFLATION, and we deserve to be at 1%, saving One Trillion Dollars a year on Interest Costs,” the president wrote on social media on Friday in a post that again took direct aim at Mr. Powell using one of his favorite nicknames. “I can’t tell you how dumb Too Late is — So bad for our Country!”

Mr. Trump has made clear that, even if he doesn’t try to fire Mr. Powell, he will pick a successor who will listen to him and cut interest rates. The Fed operates independently of the White House, a safeguard that is seen as sacrosanct to ensure that borrowing costs are set based on what is most appropriate for the economy rather than what is politically desirable.

Throughout his tenure at the Fed, Mr. Powell has strongly supported that independence. When asked about the president’s criticism at an event in Sintra, Portugal, earlier this month, the chair said he was “very focused on just doing my job.”