Inflation has remained stubbornly above the Federal Reserve's 2% target on an annual basis. But recent economic data has helped fuel a narrative that the central bank should cut rates sooner than later.

Immediately following Thursday's encouraging inflation data, which showed headline inflation falling month over month for the first time since May 2020, markets were pricing in a roughly 89% chance the Federal Reserve begins to cut rates at its September meeting, up from 75% a day prior, according to data from the CME Group.

The data is the latest to build the case for Fed rate cuts.

On Friday, the Bureau of Labor Statistics showed the labor market added 206,000 nonfarm payroll jobs last month, ahead of the 190,000-plus expected by economists. However, the unemployment rate unexpectedly rose to 4.1%, up from 4% in the month prior. It was the highest reading in almost three years.

Notably, the Fed's preferred inflation gauge, the so-called core PCE price index, showed inflation eased in May. The year-over-year change in core PCE came in at 2.6% over the prior year in May, in line with estimates and the slowest annual gain in more than three years.

"The decline in the consumer price index between May and June won’t stick but it strengthens the case for the Federal Reserve to begin cutting interest rates in September, particularly as the labor market has softened," wrote Oxford Economics chief US Economist Ryan Sweet.

Still, the economist warned, "We caution about reading too much into the decline in the CPI in June and don’t believe that this is the new trend."

Seema Shah, chief global stratgiest at Principal Asset Management, agreed the latest numbers "put us firmly on the path for a September Fed rate cut" but that "a July policy cut is still off the table."

"Not only would it spark questions of 'what do they know about the economy that we don't know?' but the Fed still needs to gather additional evidence of waning price pressures to be absolutely certain of the inflation path."

Read more on the latest CPI print here.