(Reuters) - Federal Reserve Governor Michelle Bowman softened her usually hawkish tone ever so slightly on Saturday, noting some further "welcome" progress on inflation in the last couple months even as she said inflation remains "uncomfortably above" the central bank's 2% goal and subject to upside risks.

"Should the incoming data continue to show that inflation is moving sustainably toward our 2% goal, it will become appropriate to gradually lower the federal funds rate to prevent monetary policy from becoming overly restrictive on economic activity and employment," Bowman said in remarks prepared for delivery to a closed meeting of the Kansas Bankers Association. "But we need to be patient and avoid undermining continued progress on lowering inflation by overreacting to any single data point."

The Fed at the end of July kept the policy rate in the same 5.25%-5.50% range it has been for more than a year, but signaled that a rate cut could come as soon as September if inflation continued to cool. Inflation by the Fed's targeted measure -- the year-over-year change in the personal consumption expenditures price index - eased to 2.5% in June.

Bowman's remarks did not foreclose a rate cut next month. Indeed, she noted the Fed by its September meeting will have additional economic data as well as a better idea of how recent financial market volatility may affect the economic outlook.

Bowman also did not repeat her assertion in prior speeches that she remains willing to raise rates at a future Fed meeting if needed.

But she remains a voice of caution on the Fed policy-setting committee as it moves closer to cutting interest rates.

While Bowman reiterated that her baseline outlook is for inflation to continue to decline with monetary policy held steady, she expressed skepticism that price pressures will ease as quickly this year as they did last year.

And although she said risks to the Fed's two goals of price stability and full employment are moving into better balance, she signaled she is still more worried about inflation.

The July jump in the unemployment rate, to a nearly three-year high of 4.3%, "may be exaggerating the degree of cooling in labor markets," she said, pointing to a low level of layoffs and the likelihood that Hurricane Beryl had temporarily slowed job gains.

Meanwhile, she said, risks including geopolitical tensions threaten to push up prices further. "With some upside risks to inflation, I still see the need to pay close attention to the price-stability side of our mandate while watching for risks of a material weakening in the labor market," she said.