Germany's Dax tumbled by 3% to 9,948.59, while France's Cac-40 fell 2.8% to 4,519.23 and the UK's FTSE was off by 2.7% at 6,080.20.
There were no shares rising on any of the main indexes, with mining firm Glencore among the biggest losers.
Earlier, figures for August showed factory activity in China contracting at its fastest pace in three years.
The
official manufacturing purchasing managers' index (PMI) dropped to 49.7
from 50 in July. A figure below 50 indicates contraction.
It follows recent turmoil in the markets sparked by concerns over a slowdown in the world's second-largest economy.
"The
importance of today's announcement is that the slowdown is hitting the
larger state-backed firms who typically take longer to feel the pain,"
said Josh Mahony from online trading firm IG Index.
"There are
precious few signs that China is beginning to recover, and while [the
People's Bank of China's] action can provide a temporary reprieve, we
are yet to see any evidence that it is doing any good to the economy,"
he added.
For both the UK's FTSE 100 and the US's S&P 500, August was the worst month since May 2012.
"While
a measure of calm has returned to these markets recently and they have
seen relief rallies, many of the underlying negative fundamentals are
still in place," said Nariman Behravesh, chief economist for IHS, in a
report.
"As a result, the downside risks for most commodity
prices, exchange rates and stock markets are likely to persist for some
time, while growth in many parts of the world, especially in emerging
markets, is likely to deteriorate further."
The Chinese manufacturing data also sent the price of Brent crude oil down by 3% to $52.43 a barrel, giving back some of its recent sharp gains.
Before
Tuesday's fall, the price of oil in London had risen by about 25% in
the past three trading sessions, while in the US it has risen by 27% in
the same period.
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