Wall Street shares were flat ahead of a key earnings report while stocks fell in Europe after a disappointing UK inflation report doused hopes of a quick Bank of England rate cut.
Falling copper prices also hit mining shares.
London stocks closed lower and the pound jumped on news that Britain's Consumer Prices Index rose 2.3 percent in April, slower than the previous month but outpacing analyst expectations of 2.1 percent.
"This was disappointing news, and the markets moved quickly to price out hopes of a June rate cut. It now looks as if September is most likely," said David Morrison, senior analyst at Trade Nation.
The UK inflation news comes on top of statements from US Federal Reserve members suggesting they need to see more proof that inflation is under control before cutting rates.
"Investors are now looking for the Fed to cut rates by 40 basis points by year-end, versus 56 bps by the Bank of England and 67 bps by the European Central Bank," said Luca Santos, currency analyst at ACY Securities.
In New York, the main indexes were all largely unchanged.
US shares were largely on hold ahead of a Wednesday earnings update from Nvidia -- the third-largest US company by market capitalisation -- which is sometimes seen as a gauge of overall market sentiment.
The chip-maker's stock price is up 90 percent in 2024 with its high-end processors prized by firms looking to get ahead in the booming artificial intelligence sector.
However, there is a worry that should the figures not match sky-high expectations, a sell-off coud ensue, particularly among its fellow tech firms.
"The market is geared up to hear what Nvidia reports, but more to the point, it is geared up to see how Nvidia trades after the report and the effect that has on the broader market," said Patrick O'Hare, an analyst at Briefing.com.
Shares of food-to-clothing retailer Marks & Spencer rose 3.7 percent on a strong profits report, but that was not enough to pull London's overall FTSE 100 Index higher.
Anglo American rose 0.4 percent after the London-quoted company rejected the latest bid by BHP but left the door open to further discussions.
Among other mining shares, Rio Tinto fell 2.4 percent and Glencore fell 3.6 percent.
Paris and Frankfurt indices dropped with sentiment also subdued after a mixed session in Asia.
Copper prices slumped for a second day as traders took profits on a rally that had taken it above $11,000 a tonne.
Oil prices fell for the second day and the dollar edged higher against the euro and yen.
Key figures around 1540 GMT
New York - Dow: DOWN 0.1 percent at 39,816.65
New York - S&P 500: DOWN less than 0.1 percent at 5,319.23
New York - Nasdaq Composite: UP 0.1 percent at 16,850.31
London - FTSE 100: DOWN 0.6 percent at 8,370.33 points (close)
Paris - CAC 40: DOWN 0.6 percent at 8,092.11 (close)
Frankfurt - DAX: DOWN 0.3 percent at 18,680.20 (close)
EURO STOXX 50: DOWN 0.4 percent at 5,025.17 (close)
Tokyo - Nikkei 225: DOWN 0.9 percent at 38,617.10 (close)
Hong Kong - Hang Seng Index: DOWN 0.1 percent at 19,195.60 (close)
Shanghai - Composite: FLAT at 3,158.54 (close)
Dollar/yen: UP at 156.52 yen from 156.18 yen on Tuesday
Euro/dollar: DOWN at $1.0835 from $1.0858
Pound/dollar: UP at $1.2728 from $1.2708
Euro/pound: DOWN at 85.16 from 85.41 pence
West Texas Intermediate: DOWN 0.7 percent at $78.14 per barrel
Brent North Sea Crude: DOWN 0.6 percent at $82.36 per barrel