A booming U.S. economy that is driving inflation higher around the world and pushing up the U.S. dollar is pressing some central banks to increase interest rates, despite the public health crisis and incomplete economic recoveries in their own countries.

The world's central banks are hanging on how the U.S. Federal Reserve will respond to a rise in inflation, wary of being caught in the crosscurrents of an extraordinary U.S. economic expansion. Global stock markets fell on Thursday after Fed officials signaled they expect to raise interest rates by late 2023, sooner than they anticipated in March, as the U.S. economy heats up.

A global march toward higher interest rates, with the Fed at the center, risks stifling the economic recovery in some places, especially at a time when emerging-market debt has risen.

The size of the U.S. economy, accounting for almost a quarter of world gross domestic product, and the importance of its financial markets have long exerted an outsize pull on global policy-making. But unusually brisk U.S. growth this year is critical to a world economy still recovering from last year's shocks. Fed officials expect the U.S. economy to grow 7% this year, according to projections released Wednesday.

Central banks in Russia, Brazil and Turkey have raised interest rates in recent weeks, in part to tamp down inflation stemming from the surge in commodities prices this year. As factories around the world strain to satisfy U.S. demand, commodities' prices ranging from tin to copper have soared.

"With all the consequences of the public health crisis, the last thing these countries need now is policy tightening," said Tamara Basic Vasiljev, an economist with Oxford Economics in London.

A U.S. economic boom supports economies around the world by boosting U.S. imports and remittances. But it also drives up borrowing costs and inflation and strengthens the dollar, which tightens global financial conditions and acts as a restraint on the recovery.

The pain is felt unevenly. A stronger dollar hurts emerging-market economies that have borrowed in dollars, while helping larger exporters in Europe and East Asia whose products become more competitive relative to U.S. exports.

In advanced economies, central bankers mostly believe that the period of rising inflation will prove temporary unless consumers come to expect it to continue and demand higher wages.

While central banks don't see that happening soon, some economists think they may be surprised.

"I think there is a high chance that this temporary shock to prices could become more enduring," said Luigi Speranza, chief global economist at BNP Paribas. Mr. Speranza noted that inflation in Germany is likely to be around 4% when the next round of pay bargaining starts toward the end of this year.

Central banks in Europe and Japan need to match the Fed's dovishness or risk a spike in their currencies that could undermine economic recovery, economists said. The delicate dance around the Fed could come undone if inflation proves more persistent than expected, which would likely trigger a chain reaction of interest-rate increases.

To prevent the euro strengthening the [European Central Bank] would need to be similarly dovish as the Federal Reserve, which might be a struggle due to different inflation and growth dynamics

- said Elga Bartsch, head of macro research at BlackRock.

Emerging-market economies often don't have the luxury of waiting, however. Even a short burst of inflation can weigh heavily on their currencies and hurt companies' and households' ability to service debt that is often denominated in dollars or euros.

The Fed has signaled that it will take care to avoid a repeat of the 2013 "taper tantrum," in which central banks in developing countries were forced to respond to a sudden withdrawal of foreign investment after the U.S. central bank surprised investors by saying it was considering a reduction in its stimulus programs.

So our intention for this process is that it will be orderly, methodical, and transparent, and I can just tell you, we see real value in communicating well in advance what our thinking is. And we'll try to be clear.

- Federal Reserve Chairman Jerome Powell said Wednesday. 

But with global inflation accelerating and the Fed starting to shift course, the calculus for some central banks is changing.

Brazil's central bank unveiled a third consecutive 0.75 percentage point interest rate increase on Wednesday and signaled possible larger increases ahead, as it wrestles with inflation above 8%.

The Bank of Russia has raised its benchmark rate three times this year to 5.5%, after inflation accelerated to over 6% this month, its highest level in almost five years. On Tuesday, Gov. Elvira Nabiullina said that Russia will continue raising interest rates and doesn't expect this to hinder economic growth.

"We have kept rates low for quite some time to make sure we don't clip the wings of a recovering economy," Ms. Nabiullina said in a speech at Russia's lower house of parliament. "Now is the time to raise rates in response to changed circumstances and rising inflation."

Turkey's central bank sharply increased its main interest rate to 19% in March to counter double-digit inflation and a depreciating lira. But the Turkish lira has again come under pressure in recent weeks as investors try to assess whether the central bank will heed the demands of President Recep Tayyip Erdogan to cut rates.

Recent price increases on fresh produce have raised the so-called borscht set -- the vegetables needed for Russia's beloved soup -- which is a bellwether indicator for many Russians. Since the start of the year, the price of potatoes, cabbage and carrots have risen by 60% to 80%.

In poor countries, a larger share of spending usually goes to essentials such as food and energy, so policy makers are quicker to tamp down on inflation when those prices rise.

Central banks in Scandinavia and South Korea have signaled plans to tighten monetary policy to restrain possible asset bubbles, particularly in property. Norway's central bank signaled Thursday that it will increase interest rates in September.

Central banks in central Europe, and including Hungary and the Czech Republic, are also expected to lift rates soon. They didn't suffer contractions on the same scale as larger European countries such as France and Spain during 2020, but are seeing inflation rise.

Iain Stealey, chief investment officer of fixed income at JP Morgan Asset Management, said the Fed will likely manage to avoid a repeat of the "taper tantrum."

"It is a very long, slow process...it's very difficult not to do this given upside surprises in inflation," Mr. Stealey said.

Still, there are problems with the patient approach, economists said.

"This idea of letting inflation run hot...means that you're only going to realize you have an inflation problem when you already have an inflation problem," said Klaus Baader, chief global economist at Société Générale.

Write to Tom Fairless at tom.fairless@wsj.com and Paul Hannon at paul.hannon@wsj.com