(Updates with Fed minute reaction; adds settled oil prices; updates throughout)
* Global shares recover after China downgrade
* Oil retreats, U.S. gasoline stock draw smaller than anticipated
* Treasury yield curve flattens, Wall Street remains higher
* Dollar loses vs. euro, yen
NEW YORK, May 24 (Reuters) - U.S. Treasury yields fell to session lows on Wednesday after Federal Reserve minutes signaled a gradual approach to interest rate hikes, and oil pulled back on a draw of U.S. gasoline stock that was smaller than expected.
While the yield curve flattened, Wall Street remained slightly higher and the dollar slipped after minutes from the Fed's May 2-3 meeting indicated it would gradually raise interest rates and reduce its bond reinvestment.
The yield gap between two-year and 10-year Treasuries narrowed 2 basis points to 95 basis points, Tradeweb data showed.
"Their plan is in place to gradually phase out reinvestments beginning in the fourth quarter," said Matt Toms, chief investment officer of fixed income at Voya Investment Management in Atlanta.
"Even though the Fed is reducing stimulus, I think this gives the market some comfort. It won't lift the rate structure much," he said.
Interest rate futures implied traders see about an 85-percent chance of a quarter-point rate hike at the Fed's June meeting.
The U.S. dollar index fell to session lows after the Fed minutes. It had been hovering just above its 6-/12 month lows as investors shifted from U.S. politics to monetary policy. The index was was down 0.23 percent at 97.127.
The greenback fell against the euro and the yen .
Wall Street was volatile but held on to small gains, despite the fall of banking stocks on the Fed minutes. The S&P financial index pared some losses but was still 0.14 percent lower.
The Dow Jones Industrial Average rose 49.84 points, or 0.24 percent, to 20,987.75, the S&P 500 gained 2.91 points, or 0.12 percent, to 2,401.33 and the Nasdaq Composite added 15.31 points, or 0.25 percent, to 6,154.02.
"While June seems a given for a rate hike, investors are questioning a September move, especially if economic data continue to be mixed and if inflation doesn't gain momentum," Quincy Krosby, Chief Market Strategist at Prudential Financial in Newark, in an email.
Elsewhere, world stock markets recovered from initial losses after Moody's Investors Service issued its first credit downgrade of China in 30 years, dropping China's sovereign debt to A1 from Aa3.
The pan-European FTSEurofirst 300 index rose 0.01 percent and MSCI's gauge of stocks across the globe gained 0.09 percent.
Emerging market stocks rose 0.25 percent. MSCI's broadest index of Asia-Pacific shares outside Japan closed 0.13 percent higher, while Japan's Nikkei rose 0.66 percent.
Oil prices fell slightly after the Energy Information Administration said U.S. crude oil inventories fell for the seventh straight week.
U.S. crude oil futures settled 11 cents, or 0.21 percent, lower at $51.36 per barrel. Brent crude was last down 0.39 percent, or 21 cents at $53.94.
Investors await the outcome of discussions in Vienna between OPEC and other oil-exporting countries on whether to extend output cuts.
(Additional reporting by Jamie McGeever in London, Saqib Iqbal Ahmed, Richard Leong, Caroline Valetkevitch and Jessica Resnick-Ault in New York; Editing by Nick Zieminski)