(Reuters) - U.S. economic activity expanded at a slight to modest pace from late May through early July and firms reported some signs that the jobs market continues to soften, underscoring the Federal Reserve's recent pivot to more keenly assessing slowing demand for labor to ensure it doesn't wait too long before cutting interest rates.

The U.S. central bank's latest temperature check on the health of the economy also showed that inflation pressures increased at a modest pace.

"Economic activity maintained a slight to modest pace of growth in a majority of Districts this reporting cycle," the Fed said in its survey released on Wednesday, which polled business contacts across the central bank's 12 districts through July 8. "While seven Districts reported some level of increase in activity, five noted flat or declining activity - three more than in the prior reporting period."

The analysis, released roughly every six weeks, comes as Fed Chair Jerome Powell and his colleagues have emphasized that risks on inflation and jobs are now in balance. Earlier on Wednesday two top Fed officials said interest rate cuts are "getting closer," remarks that appear to set the stage for a lowering of borrowing costs in September.

After being stung by higher-than-expected inflation in the first part of this year, Fed officials have been encouraged by more positive readings in April, May and June. Inflation remains, by the Fed's preferred measure, at 2.6%. The next release of that gauge is due on July 26.

As disinflation has resumed, Fed officials have more strongly spoken about a marked deterioration in the labor market as a reason the central bank would begin to cut its policy rate.

Several districts noted softer labor market conditions. A Wisconsin source told the Minneapolis Fed there were "still plenty of job openings," but employers were raising hiring standards and pausing on some hires, the bank reported.

The Fed is trying to engineer a so-called "soft landing" for the economy in which economic growth gradually slows and the unemployment rate remains low even as inflation, which spiked to a 40-year high two years ago, returns to the Fed's 2% target rate.

The unemployment rate hit a 2-1/2-year high of 4.1% in May and annual wages increased at the slowest pace in three years amid an expanding labor pool, the latest government data showed.

The Fed's benchmark overnight lending rate has been held in the range of 5.25% to 5.50% for the past year. While policymakers have all but ruled out a cut at the upcoming meeting on July 30-31, investors currently expect the Fed to lower borrowing costs in September, November and December this year.