* European stock markets fall, Wall Street indexes rise
* Oil rallies, Treasury yields rise with rates in focus
* U.S. inflation data to test market doves
NEW YORK Dec 18 (Reuters) - MSCI's global equity index was advancing slightly while oil prices rallied on supply concerns and U.S. Treasury yields rose as investors digested mixed messages from the Federal Reserve about the prospects for 2024 interest rate cuts.
Oil prices climbed after Iranian-backed Houthi militants stepped up attacks on vessels in the Red Sea, raising concerns about supply disruptions although ample supply and scepticism around Russia's plan to cut exports in December limited gains.
Chicago Federal Reserve President Austan Goolsbee on Monday pushed back against market bets on interest rate cuts. Also pushing back against expectations for cuts on Monday was Cleveland Fed President Loretta Mester, who votes on policy in 2024 until her June retirement.
But this was after investors had celebrated on Wednesday and Thursday after dovish comments from Fed chair Jerome Powell when the central bank's meeting ended on Wednesday with officials pencilling in expectations for rate cuts.
Pushbacks on bets the Fed would pivot to cutting had started on Friday when the Fed's New York President John Williams said it was "premature" to speculate about rate cuts.
"Powell seemed to be pretty sure in what he was saying. Then you had the New York Fed muddy the water on Friday," said Robert Pavlik, senior portfolio manager at Dakota Wealth in Fairfield, Connecticut, also citing Goolsbee's comments.
"On Thursday there was an immediate need to reallocate your portfolio because the Fed was pivoting. Then Friday you had a New York Fed official pour cold water on it. That leaves you without a pressing need to make changes today," said Pavlik.
On Wall Street, The Dow Jones Industrial Average rose 59.54 points, or 0.16%, to 37,364.7, the S&P 500 gained 25.25 points, or 0.54%, to 4,744.44 and the Nasdaq Composite added 76.20 points, or 0.51%, to 14,890.12.
The pan-European STOXX 600 index lost 0.27% and MSCI's gauge of stocks across the globe gained 0.14%.
Longer-dated U.S. Treasury yields rose in reaction to Goolsbee's comments on Monday.
Benchmark 10-year notes were up 3.2 basis points to 3.960%, from 3.928% late on Friday. The 30-year bond was last up 4.2 basis points to yield 4.0688%, from 4.027%. The 2-year note was last was up 1 basis points to yield 4.4653%, from 4.455%.
However, the U.S. dollar eased against the euro, extending last week's fall, as the U.S. currency remains under pressure from last week's signals about the possibility of rate cuts.
The dollar index fell 0.058%, with the euro up 0.23% to $1.0919. The Japanese yen weakened 0.61% versus the greenback at 143.04 per dollar, while Sterling was last trading at $1.2633, down 0.33% on the day.
In the United States, a reading on core personal consumption expenditure (PCE) index due on Friday is forecast by analysts to rise 0.2% in November with the annual inflation rate slowing to its lowest since mid-2021 at 3.4%, according to Reuters polling. Also on investors' watch lists this week is the Bank of Japan's policy decision on Tuesday with April favoured by 17 of 28 economists as the kick-off for negative rates to be scrapped, making the BOJ one of the few central banks in the world actually tightening.
Oil rose after the Yemeni Houthi militant group Red Sea attacks disrupted maritime trade. Oil major BP said it temporarily paused transit there and other shipping firms also said they would avoid the route.
U.S. crude recently rose 2.58% to $73.27 per barrel and Brent was at $78.57, up 2.64% on the day. (Additional reporting by Nell Mackenzie and Wayne Cole; Editing by Amanda Cooper, Jacqueline Wong, Hugh Lawson and Josie Kao)
