JACKSON HOLE, Wyo. — The Federal Reserve and other central banks are entering their most perilous chapter since the 2008 financial crisis, as they come under enormous pressure to keep the global economy out of recession while questions mount about their power to do so.

Even as he promised to “act as appropriate to sustain the expansion,” Fed Chair Jerome H. Powell warned Friday that the escalating trade war with China was a “complex, turbulent” situation and that the Fed did not have a playbook for counteracting the economic hit it was delivering to the U.S. and global economies.

“While monetary policy is a powerful tool that works to support consumer spending, business investment and public confidence, it cannot provide a settled rule book for international trade,” Powell said at an annual conference of central bankers here. “Trade policy uncertainty seems to be playing a role in the global slowdown and in weak manufacturing and capital spending in the United States.”

President Trump, who has called for Powell to move swiftly to cut interest rates, reacted with fury to his comments. “My only question is, who is our bigger enemy, Jay Powell or Chairman Xi?” he tweeted after the speech, referring to Chinese President Xi Jinping.

The exchange encapsulated the dramatic collision of politics and economic policy buffeting the global economy. Politicians, including Trump and other leaders in Europe and Asia, are reversing decades of efforts to deepen trade and business ties among nations. That is causing high anxiety among corporate leaders, who are pulling back on spending, and investors, who are seeking ultrasafe places to park money, causing alarm bells in the financial markets.

At the same time, central banks, traditionally run by economists and technocrats untethered from politics, are being pressed to lower interest rates and pursue other monetary policies that would encourage economic activity and keep growth healthy. Dozens of central banks have cut rates this year, and yields on government bonds in many countries are near historic lows or even negative.

Yet there is concern from prominent quarters that this will prove inadequate to overcome the anxiety caused by the trade war and deeper fears that a long-running economic expansion will come to an end.

“Global momentum remains soft, despite the broad-based easing in global monetary expectations,” said Mark Carney, head of the Bank of England.

Lawrence Summers, who was treasury secretary for President Bill Clinton and economic consigliere for President Barack Obama, summarized the concern in a tweet that made a splash at the Fed conference here:

“Coming into Jackson Hole, economists are grappling with a major issue: Can central banking as we know it be the primary tool of macroeconomic stabilization in the industrial world over the next decade?”

He titled the approach of central banks “black hole monetary economics” to underscore the fact that interest rates are already near zero — with little to show for it.

Greg Mankiw, former chief economist for President George W. Bush and a longtime Republican economic policy adviser, sounded a similar alarm in an email interview.

“Not all of the effects of the trade war can be offset by more expansionary monetary policy,” he said. “In particular, to the extent that rising tariffs disrupt global supply chains, the result is an adverse effect on the supply of goods and services. There is nothing monetary policy can do to reverse that.”

As central bankers look to stimulate growth, however limited the effect may be, political leaders are continuing to take steps that are stymieing activity, many economists say. Trump’s trade war has led to a decline in U.S. business investment, and the manufacturing sector has seen some of its worst numbers in a decade.

Under new Prime Minister Boris Johnson, Britain is at increasing odds of a “hard” exit from the European Union. Some leaders in Europe are also increasingly referencing the possibility of other nations leaving the E.U. And trade ties between other nations, such as between Japan and South Korea, are coming under stress.

Economists such as Summers argue that it is the responsibility of elected leaders, not central bankers, to take steps to rev up growth in ways that have never been fully embraced since the 2008 financial crisis and recession. For example, he wrote on Twitter, elected officials could invest in infrastructure or redistribute more income from the rich to the middle class and poor, who are more likely to spend it.

The risk of an overreliance on central banks is that they disappoint and draw worse political fire. Economists have long argued that central banks’ independence from politics has meant they could do the right thing for the economy irrespective of short-term political impact.

If this were to be compromised, the argument goes, markets could lose faith in the power of central banks to stabilize the economy during crisis, creating worse crises. The Fed faced criticism in the aftermath of the 2008 crisis for bailing out banks, but the tenor of the critiques was never as harsh as what’s coming from Trump, even though he selected Powell for the top Fed job in 2017.

“The problem is not in the [monetary system]; it’s in the president of the United States,” Stanley Fischer, former vice chair of the Federal Reserve, told his colleagues Friday at lunch. “I have no idea how to deal with this.”

The Fed’s main tool to affect the economy is its benchmark interest rate, which influences lending in many sectors. Powell led the Fed to cut it by a quarter point — to a range of 2 to 2.25 percent — last month. Powell described the move as protective against an economic decline, but there wasn’t universal support for it.

The Fed historically has cut rates only in times of significant economic stress, not when unemployment is at a very low 3.7 percent. The decision to cut means the Fed has that much less room to reduce rates further if the economy does fall into a recession.

The Fed’s sister institutions, including the European Central Bank, are in a similar predicament.

“The central banks back to the financial crisis — that was before my time — they did a great job,” Øystein Olsen, head of the central bank of Norway, said in an interview. “In Europe, the ECB was the only player in town, but it is a worry that it continues in that way, as if central banks can solve every problem coming up.”

The U.S. economy is currently one of the strongest in the world, even though it is slowing and more cracks are opening up. Nine other major economies are in recession or close to it. China, even though it is still growing fast by conventional standards, has slowed sharply.

This global slowdown, combined with the actions of central banks around the world, is causing disturbances in financial markets.

In Europe and Japan, numerous government and corporate bonds now trade with negative yields, meaning investors can expect to be paid less than they invest — an exchange they’re willing to make for the sake of being assured repayment.

In the United States, government bond yields inverted several times this week, an unusual situation that upends the normal expectation that people get higher returns for investing their money for longer. The “inverted yield curve” has always preceded a recession, though often by a year or longer.

While Trump often directs his criticism at Powell, a committee currently consisting of 17 people debates interest rate policy, and 10 get to vote.

Trump is calling for a one-point reduction in interest rates when the Fed meets next in September, but Fed leaders remain divided over whether a cut is even necessary.

“Nothing is moving dramatically in a negative direction,” Philadelphia Fed President Patrick Harker said in a CNBC interview. “I think we need to keep our powder dry so when that happens we have the policy space to move.”

At the other end of the spectrum, James Bullard, president of the Federal Reserve Bank of St. Louis, is urging consideration of a half-point reduction in rates, more than the quarter-point investors expect.

“I think it will at least be discussed whether we should try to be more aggressive than that,” Bullard said. “It will be a robust debate.”

Even if he favors a sharper cut, he says the harshness of the critique by Trump is unusual.

“Unemployment is close to a 50-year low. Inflation, I think, is a little low … but it’s not too bad compared to historical data, so it’s kind of a funny time to have the Fed open to a lot of criticism,” Bullard said.

Correction: An earlier version of this story misspelled the name of Philadelphia Fed President Patrick Harker. This has now been corrected.