WASHINGTON, July 29 (Reuters) - President Donald Trump on Wednesday refused to turn on his "brilliant" hand-picked U.S. central banker in chief despite the fact that Federal Reserve Chairman Kevin Warsh has not delivered the rate cuts Trump desperately wants and has dim prospects for doing so anytime soon.

"He's a brilliant guy," Trump told reporters in the Oval Office. "I know he'd love to see lower interest rates, but he's got a board, and it's a political board, and they want to keep rates up. But we fight through rates."

Warsh, to the contrary, hinted at a press conference following the Fed's decision to leave rates unchanged that he may in fact be more inclined toward rate hikes as the appropriate response to the stiffening inflation now occurring alongside a resilient job market and economy.

"Any central banker, especially a central banker where the labor markets are more or less at equilibrium ... any central banker, when he or she sees underlying inflation moving higher, he or she is more inclined to tighten policy. Again, when you've achieved the other side of your mandate and you see underlying inflation falling, he's more inclined to loosen policy," Warsh said. "That's my reaction function."

Trump's remarks came on the heels of the second Fed policy decision since Warsh took over in May from Jerome Powell, whom Trump relentlessly attacked for not cutting rates aggressively as he repeatedly demanded. In both instances, the Fed has held rates steady in a range of 3.50% to 3.75%, but at this week's meeting three of Warsh's new colleagues dissented in favor of a rate hike.

And indeed, that may well be the next action delivered by the Warsh Fed: Rate futures markets currently see greater than a 60% probability of a quarter-point increase when central bankers meet again in September.