Donald J. Trump attacked the Federal Reserve on Monday night before the largest audience he has yet addressed, telling the millions of people watching the first presidential debate that the nation’s central bank is acting as an arm of the Democratic Party at the expense of the economy.

It is an extraordinary accusation, backed by no evidence, that plows across a bipartisan line. Since the 1970s, presidential candidates and presidents have avoided publicly criticizing the Fed’s decisions about raising and lowering interest rates.

Mr. Trump, the Republican presidential nominee, said that Janet L. Yellen, the Fed’s chairwoman, was “doing political things” by holding interest rates at low levels. He said that the American economy was in a “big, fat, ugly bubble” that would pop when the Fed started raising rates. Ms. Yellen, he said, was waiting until President Obama left office.

This accusation, which Mr. Trump has leveled several times in recent weeks, is roundly rejected by Fed officials — including those who agree it is time to raise interest rates. It is also rejected by a wide range of independent observers.