By Sinéad Carew and Alun John

NEW YORK/LONDON (Reuters) -A global equities gauge fell slightly on Tuesday while U.S. Treasury yields rose to multi-week peaks as investors waited cautiously for inflation data due later in the week with hopes for clues on the outlook for U.S. interest rates.

U.S. Treasury yields gained ground after a weak auction. They had risen earlier after data showed U.S. consumer confidence unexpectedly improved in May amid optimism about the labor market after deteriorating for three consecutive months.

In addition, U.S. house price growth slowed sharply in March, likely as rising mortgage rates weighed on demand.

Equity investors were most focused on waiting for price data that is not due out until Friday. The Federal Reserve's preferred inflation barometer, the U.S. core Personal Consumption Expenditures Price Index report, is expected to hold steady on a monthly basis for April.

"It's a holiday-shortened week so volume is likely to be pretty low all week. That's combined with the fact that markets are focused on one key data point due out Friday," said Gene Goldman, chief investment officer at Cetera Investment Management in El Segundo, California, referring to Monday's U.S. Memorial Day holiday.

"The market is anxiously sitting on the sidelines waiting to get confirmation that inflation is slowing towards the Fed's target," Goldman said.

MSCI's gauge of stocks across the globe fell 1.28 points, or 0.16%, to 792.07.

Still, on Wall Street, the Nasdaq managed to rise past 17,000 level, and close above it for the first time as AI leader Nvidia hit a record high.

The Dow Jones Industrial Average fell 216.73 points, or 0.55%, to 38,852.86, the S&P 500 gained 1.32 points, or 0.02%, to 5,306.04 and the Nasdaq Composite gained 99.09 points, or 0.59%, to 17,019.88.

Earlier Europe's STOXX 600 index closed down 0.6%.

In Treasuries, yields rose after two lackluster debt auctions raised doubts about demand for U.S. government debt while investors also digested the economic data, which fueled uncertainty about the Fed's monetary policy outlook.

"With $297 billion in nominal supply on Tuesday between coupons and bills, I think some indigestion is to be expected," said Tom Simons, U.S. economist at Jefferies in New York.

The yield on benchmark U.S. 10-year notes rose 6.7 basis points to 4.54%, from 4.473% late on Friday, while the 30-year bond yield rose 7.9 basis points to 4.656%.

The 2-year note yield, which moves in step with interest rate expectations, rose 2.1 basis points to 4.9742%.