NEW YORK, July 30 (Reuters) - Investors searching for clarity from a newly led U.S. Federal Reserve were disappointed on Wednesday, warning that the central bank's mixed messages on the outlook for interest rates could unsettle stocks and bonds and increase the risk of market volatility.

The Fed kept interest rates unchanged in a target range of 3.50% to 3.75%. The vote drew three dissents from the 12-member panel, leading analysts to characterize the decision as a "hawkish hold" that leaves the door open to future rate hikes.

With President Donald Trump's new Fed chair, Kevin Warsh, abandoning the practice of holding investors' hands through forward guidance, markets have entered a new paradigm. Investors are now combing through economic data for any signal of the Fed's next move, a dynamic that many say could trigger sharper bouts of volatility.

Markets headed into the meeting pricing in a roughly 36% chance of a rate hike, making it the most uncertain Fed decision since December 2018, according to Deutsche Bank.

"Each meeting we're now building more uncertainty around it than the last," said JP Powers, chief investment officer at RWA Wealth Partners.

"It looks like September now -- maybe we're building to that crescendo -- but we'll have to see how the data shakes out now over the interim."

U.S. consumer inflation slowed to 3.5% in June but remains well above the Fed's 2% target. At the same time, renewed U.S.-Iran tensions, which escalated again this month, threaten another oil-driven rebound in price pressures.

In a press briefing after the meeting, Warsh said officials were not committing to any immediate action, but stressed that policymakers "will not hesitate to act" at upcoming meetings if price pressures fail to ease.

Yet as Warsh fielded reporters' questions, concerns about policy uncertainty were compounded by a more fundamental issue: whether the Fed chair has a clear and coherent roadmap for returning inflation to the 2% goal that he said remains the hard target.

Calvin Tse, head of U.S. strategy and economics at BNP Paribas, said a jump in long-term Treasury yields on the news was a clear message from the market to Warsh that he should act.

"If he is tough on inflation as he says, why has he not already acted? That seems to be the question," he said.

Following the meeting, futures markets briefly priced in a 77% chance of a September rate increase before pulling back to about 57% by late Wednesday, according to the CME's FedWatch tool, with about 35 basis points of hikes expected by the end of 2026.

HEADWIND FOR STOCKS AND BONDS

The Fed decision weighed on U.S. stocks, while shorter-dated Treasury yields fell as investors unwound earlier bets on a July rate increase that had been assigned an unusually high probability before the policy meeting.

A "hawkish hold" is typically a headwind for stocks because it signals borrowing costs could remain elevated longer than investors had anticipated, analysts said. Some investors also worry that delaying action now could ultimately force the Fed into more aggressive tightening later.

Trump has repeatedly called for the Fed to lower rates but praised Warsh on Wednesday despite his decision to hold. Warsh, for his part, has said monetary policy should be independent.

Any relief for stocks from the Fed not hiking "tends to be very short-lived, and tends to be offset by the realization that...there's going to be more inflation," said Ed Al-Hussainy, portfolio manager, fixed income and macro, at Columbia Threadneedle Investments. "That's corrosive for returns, especially when you're starting at valuations that are not cheap."

The prospect of additional rate hikes can also curb risk-taking and make safer assets such as money market funds and shorter-dated Treasuries such as bills more attractive relative to equities.

For bond markets, a pause coupled with the possibility of future hikes keeps upward pressure on yields, particularly on policy-sensitive maturities such as two-year Treasuries. A hike lifts expectations for borrowing costs, increasing the compensation investors demand to hold fixed-income securities.

Zachary Griffiths, head of macro and investment grade strategy at CreditSights, said Treasury yields have repriced higher over the past two months without any action from the Fed, effectively tightening financial conditions on the central bank's behalf.

For the month of July, the 10-year yield has risen by nearly 27 basis points, the largest monthly increase since March.

The rate move underscores how investors themselves are increasingly shaping financial conditions, a development consistent with Warsh's view that markets rather than Fed officials should play a larger role in setting expectations for rates and inflation.

Warsh "is trading forward guidance for market guidance; he's allowing markets to find the right level for interest rates and inflation," said Michael Arone, chief investment strategist, State Street Investment Management.

The need to parse data more closely, rather than rely on Fed policymakers to highlight what matters most, "is a muscle that the market is going to have to get used to using again," Arone said.