WASHINGTON (Reuters) -The case for a U.S. interest rate cut remains unresolved as Federal Reserve officials head into their policy meeting later this month, with data showing fresh signs of higher inflation and President Donald Trump intensifying his demands for lower borrowing costs.

Trump appeared near the point of trying to fire Fed Chair Jerome Powell this week, but backed off with a nod to the market disruption that would likely follow, and the U.S. central bank's policy rate outlook remains virtually unchanged despite the drama. Fed officials haven't mentioned raising rates, but headlines about an imminent Powell firing caused U.S. Treasury yields to jump, not exactly what Trump wants as he yearns for cheaper financing for massive federal deficits.

The Fed, though, is tasked with keeping inflation stable, not lowering government financing costs, and it is expected to hold its benchmark rate steady in the 4.25%-4.50% range at its July 29-30 meeting. The Fed last cut rates in December, after which it began factoring in the possible impact on prices from import tariffs that Trump quickly began imposing after returning to the White House in January.

Rate cuts are expected to resume later this year, with investors anticipating a quarter-percentage-point reduction in September.

But those odds slipped to nearly 50-50 this week after the Consumer Price Index showed inflation rose to 2.7% in June from 2.4% in the prior month. A trend that saw declining prices for goods is beginning to shift, adding to overall inflation, in a sign businesses may have begun passing some of the tariffs along to consumers.

Powell and other Fed officials said they expected price increases to quicken this summer. They have been reluctant to cut rates until it is clear how much inflation is in train, how long it persists, and whether the economy begins to slow enough to ease the pressure on prices.

Fed policymakers will receive two more months of jobs and inflation data before their meeting in September, and investors - and Trump administration officials - will be listening closely to Powell's post-meeting press conference on July 30 for language that leans towards a rate cut then or not.

In the final comments before policymakers begin a "blackout" period on public statements before the next meeting, the focus remained largely on inflation and how June's uptick showed prices rising across an array of largely imported goods.

Trade and tariff issues are now "the key drivers of the U.S. economic outlook," Fed Governor Adriana Kugler said on Thursday, adding that with price pressures building, the central bank needed to keep rates steady "for some time" to hold inflation and inflationary psychology in check.

"I see upward pressure on inflation from trade policies, and I expect additional price increases later in the year," she said. Maintaining tight monetary policy for now "is important to keep longer-run inflation expectations anchored."

Fed Governor Christopher Waller, mentioned as a possible replacement for Powell, in comments later on Thursday disagreed, repeating his call for a rate cut at the meeting in two weeks to account for what he sees as a coming economic slowdown and the likelihood that the impact of tariffs on inflation won't last.

"With inflation near target and the upside risks to inflation limited, we should not wait until the labor market deteriorates before we cut the policy rate," Waller said in prepared remarks for a speech to the Money Marketeers of New York University.

'INFLECTION POINT'

The Fed used a historically rapid escalation of interest rates in 2022 to help contain a surge of inflation in the aftermath of the COVID-19 pandemic.

By last fall, Fed officials were confident enough that inflation was receding towards the central bank's 2% target that they began to lower rates, delivering three cuts in the final four months of the year.

Trump made criticism of high inflation a centerpiece of his 2024 presidential campaign, pledging that prices would actually fall on his watch while also promising to raise tariffs.

As Trump's inauguration arrived, the economy was still growing above trend and the labor market remained tight. Fed officials and staff worried that while tariffs, like any tax, should in theory have only a one-time price impact, those conditions coupled with the recent bout of high inflation could lead to a more persistent problem.

The focus on tariffs as a source of inflation and a reason for delaying rate cuts has been central to Trump's ire at Powell, but U.S. central bankers this week said the CPI data for June showed why they are concerned, with inflation still above target and possibly poised to move higher.

Kugler estimated that coming data will show the Personal Consumption Expenditures Price Index the Fed uses for its inflation target increased 2.5% in June, while the "core" measure excluding food and energy items rose 2.8%, higher than in May.

"We may be at an inflection point," as far as inflation is concerned, Atlanta Fed President Raphael Bostic told Fox Business a day after the CPI release. Nearly half of goods saw price increases that annualize to 5% or more, he said, a ratio he uses to monitor inflation's breadth during the pandemic surge. That was double the share in January.

"The headline number moved away from our target, not towards it ... We've seen the highest increase in prices that we've seen all year," Bostic said. "We are seeing things underlying in the economy that suggest inflation pressures are up ... The price pressures are real."

In economic projections issued in June, Fed officials expected PCE inflation to hit 3% by the end of this year but still anticipated being able to cut rates by half a percentage point - far short of the massive reduction Trump wants with his call for a 1% Fed rate.

No Fed official has endorsed that Trump idea, with caution still the favored approach.

"It's important to note that it's still early days for the effects of tariffs, which take time to come into full force," New York Fed President John Williams said this week. "Though we are only seeing relatively modest effects of tariffs in the hard aggregate data so far, I expect those effects to increase in coming months."