NEW YORK, June 6 (Reuters) - Oil prices eased about 1% on Tuesday as worries that sluggish global economic growth could reduce energy demand outweighed Saudi Arabias pledge to deepen output cuts.

Brent futures fell 42 cents, or 0.6%, to settle at $76.29 a barrel, while U.S. West Texas Intermediate (WTI) crude fell 41 cents, or 0.6%, to settle at $71.74.

Prices rose on Monday after Saudi Arabia said over the weekend it would cut output to around 9 million barrels per day (bpd) in July from about 10 million bpd in May.

Saudi Arabia, the worlds top oil exporter, also unexpectedly increased the official selling price of its crude to Asian buyers.

However, the Saudi supply cut is unlikely to achieve a "sustainable price increase" into the high $80s and low $90s due to weaker demand, stronger non-OPEC supply, slower economic growth in China and potential recessions in the U.S. and Europe, Citi analysts said in a note.

The U.S. dollar rose to its highest level against a basket of currencies since hitting a 10-week high on May 31 as investors waited on fresh signals on whether the U.S. Federal Reserve will raise or hold interest rates in June.

A stronger dollar can weigh on oil demand by making the fuel more expensive for holders of other currencies.

One of those signals came from the U.S. services sector, which barely grew in May as new orders slowed.

"Crude prices are heavy as global growth concerns continue to suggest a much weaker crude demand outlook," said Edward Moya, senior market analyst at data and analytics firm OANDA.

The mood was further dented by data showing German industrial orders fell unexpectedly in April.

The World Bank, however, raised its 2023 global growth outlook as the U.S., China and other major economies have proven more resilient than forecast, but said higher interest rates and tighter credit will take a bigger toll on next years results.

Higher interest rates boost borrowing costs, which can slow the economy and reduce oil demand.

The market is awaiting data from the U.S. and China that could provide fresh demand indications in the worlds two biggest oil consumers.

China, the second-biggest oil consumer, will release its May trade data on Wednesday.

The Energy Information Administration (EIA) projected U.S. crude output will rise from 11.9 million bpd in 2022 to 12.6 million bpd in 2023 and 12.8 million bpd in 2024, That compares with a record 12.3 million bpd in 2019.

EIA also projected U.S. petroleum demand would rise from 20.3 million bpd in 2022 to 20.4 million bpd in 2023 and 20.7 million bpd in 2024. That compares with a record 20.8 million bpd in 2005, according to EIA data going back to 1973.

The market is also waiting for U.S. oil inventory data from the American Petroleum Institute (API), an industry group, at 4:30 p.m. EDT on Tuesday and the EIA at 10:30 a.m. EDT on Wednesday.

Analysts forecast U.S. energy firms added about 1.0 million barrels of crude into storage during the week ended June 2, according to a Reuters poll. ,

That would be the second weekly increase in crude stocks in a row and compares with a rise of 2.0 million barrels in the same week last year and a five-year (2018-2022) average increase of 2.3 million barrels.