By Ann Saphir and Lindsay Dunsmuir

(Reuters) -Federal Reserve Chair Jerome Powell on Monday delivered his most muscular message to date on his battle with too-high inflation, saying the central bank must move "expeditiously" to raise rates and possibly "more aggressively" to keep an upward price spiral from getting entrenched.

In remarks that sent financial markets scrambling to recalibrate for a higher probability of the Fed lifting interest rates by a half-percentage point at one or more of its remaining meetings this year, Powell signaled an urgency to the central bank's inflation challenge that was less visible than just a week ago, when the Fed delivered its first rate hike in three years.

"The labor market is very strong, and inflation is much too high," Powell told a National Association for Business Economics conference. "There is an obvious need to move expeditiously to return the stance of monetary policy to a more neutral level, and then to move to more restrictive levels if that is what is required to restore price stability."

In particular, he added, "if we conclude that it is appropriate to move more aggressively by raising the federal funds rate by more than 25 basis points at a meeting or meetings, we will do so."

AIG's global head of strategy, Constance Hunter, called it Powell's "the buck stops here" speech.

U.S. stocks fell, and traders -- already betting on at least a quarter-point interest rate increase at each of the year's remaining six Fed meetings -- moved to price in a better-than even chance of half-point interest rate increases at each of the Fed's next two meetings in May and June.

That would lift the short-term policy rate - pinned for two years near zero - to a range of 2.25% to 2.5% by the end of the year, higher than the 1.9% that Fed policymakers just last week anticipated.

Most Fed policymakers see the "neutral" level as somewhere between 2.25% and 2.5%.

Powell repeated on Monday that the Fed's reductions to its massive balance sheet could start by May, a process that could further tighten financial conditions.

"This is not just going to be a near-term tactical phenomenon," said Kevin Flanagan, head of fixed income strategy at WisdomTree Investments in New York. "This is a more strategic type of messaging, I think, from the Fed."

A consensus for more aggressive tightening - or at least an openness to it - appears to be growing.

Atlanta Fed President Raphael Bostic, who expects a slightly gentler path of rate increases than most of his colleagues, said earlier on Monday he is open to bigger-than-usual rate hikes "if that's what the data suggests is appropriate."

Speaking on Friday, Fed Governor Chris Waller said he would favor a series of half-percentage point rate increases to have a quicker impact on inflation.

TIGHT LABOR MARKET, INFLATION RISKS

The U.S. unemployment rate currently is at 3.8% and per-person job vacancies are at a record high, a combination that's pushing up wages faster than is sustainable.

"There’s excess demand," Powell said, adding that "in principle" less accommodative monetary policy could reduce pressure in the labor market and help stabilize inflation without pushing up unemployment, generating a "soft landing" rather than a recession.

Inflation by the Fed's preferred gauge is three times the central bank's 2% goal, pushed upward by snarled supply chains that have taken longer to fix than most had expected and that could get worse as China responds to new COVID-19 surges with fresh lockdowns.

Adding to the pressure on prices, Russia's war in Ukraine is pushing up the cost of oil, threatening to move inflation even higher. The United States, now the world's biggest oil producer, is better able to withstand an oil shock now than in the 1970s, Powell noted.

Although the Fed in normal times would not likely tighten monetary policy to address what in the end may be a temporary spike in commodity prices, Powell said, "the risk is rising that an extended period of high inflation could push longer-term expectations uncomfortably higher."

Last year, the Fed repeatedly forecast that supply chain pressures would ease and then was repeatedly disappointed.

"As we set policy, we will be looking to actual progress on these issues and not assuming significant near-term supply-side relief," Powell said on Monday. Policymakers began this year expecting inflation would peak this quarter and cool in the second half of the year.

"That story has already fallen apart," Powell said. "To the extent it continues to fall apart, my colleagues and I may well reach the conclusion we'll need to move more quickly and, if so, we'll do so."

Fed policymakers hope to rein in inflation without stomping on growth or sending unemployment back up, and their forecasts released last week suggest they see a path for that, with the median view for inflation falling to 2.3% by 2024 but unemployment still at 3.6%.

Powell said he expects inflation to fall to "near 2%" over the next three years, and that while a "soft landing" may not be straightforward, there is plenty of historical precedent.

"The economy is very strong and is well-positioned to handle tighter monetary policy," he said, adding that he doesn't expect a recession this year.

It is a difficult trick to finesse, analysts said.

Powell was "reasonably forthcoming that there’s uncertainty," said Seth Carpenter, chief global economist at Morgan Stanley. "If you keep going until you see the outcome that you desire, chances are you’ve gone too far."

(Reporting by Ann Saphir and Lindsay DunsmuirAdditional reporting by Herb LashEditing by Paul Simao and Alistair Bell)