(Adds U.S. market open, byline, dateline; previous LONDON)
* Wall Street, European shares slip but still near record highs
* Oil slips on oversupply worries despite OPEC deal
By Herbert Lash
NEW YORK, May 30 (Reuters) - Oil prices slid on Tuesday on concerns of a persistent global supply glut while U.S. and European political worries combined to subdue investor sentiment and weaken equity markets around the world.
The dollar fell against most currencies, weighed by a drop in U.S. Treasury yields after U.S. inflation data reinforced the notion that the Federal Reserve will only raise interest rates one more time in 2017.
Shares on Wall Street, in addition to Germany's DAX index and Britain's FTSE, are trading near record highs, which is keeping stocks from moving higher as political uncertainty picks up on both sides of the Atlantic.
Shan Osborne, chief FX strategist at Scotia in Toronto, said there is a whiff of risk aversion about the equity markets in Japan, Europe and on Wall Street fell. Markets in China and Hong Kong were closed for holidays.
U.S. President Donald Trump is considering wider staff changes amid growing political fallout over U.S. probes into Russia and his presidential campaign. A senior aide to Trump resigned on Tuesday.
"The uneasiness created by the political situation just continues to leave the market troubled over where this is all headed," said Rick Meckler, president of hedge fund LibertyView Capital Management LLC in Jersey City, New Jersey.
Continued low interest rates and reasonably good earnings are positive, but for investors to commit new money there need to be some changes, such as tax proposals and healthcare, the Trump administration had promised, Meckler said.
"They do seem just really bogged down in political battles," he said.
On Wall Street, the Dow Jones Industrial Average fell 36.22 points, or 0.17 percent, to 21,044.06. The S&P 500 lost 2.84 points, or 0.12 percent, to 2,412.98 and the Nasdaq Composite dropped 3.84 points, or 0.06 percent, to 6,206.35.
In Europe, the pan-regional FTSEurofirst 300 index of leading shares fell 0.23 percent to close at a provisional 1,533.49.
MSCI's gauge of stocks across the globe shed 0.08 percent.
Signs that elections in Italy may come as early as September weighed on stocks and initially on the euro. British blue chips fell slightly less than two weeks before a general election that will shape talks for the country's exit from the European Union.
The dollar index was down 0.18 percent at 97.271, with the euro was up 0.2 percent at $1.1186.
Against the safe-haven yen, the dollar dropped 0.4 percent to 110.79 yen.
Tuesday's U.S. economic data, while mixed, still backed the expectation that the Fed will raise interest rates next month, analysts said.
Benchmark Brent crude dropped to a low of $51.19 before recovering ground to trade down 86 cents at $51.44.
The Organization of the Petroleum Exporting Countries and other oil producers, including Russia, agreed last week to keep a tight rein on supply until the end of the first quarter of 2018, nine months longer than originally planned.
"The oil market remains on the back foot," said Stephen Brennock, analyst at London brokerage PVM Oil Associates.
Benchmark 10-year Treasuries were last up 7/32 in price to yield 2.2237 percent.
Reporting by Herbert Lash; Editing by Nick Zieminski