Stocks have fallen on fears over the health of the global economy, after last week's weak US jobs data and persistent fears over the eurozone.
The US Dow Jones index fell 1.7%, its worst day so far this year.
Earlier, France's Cac 40 fell 3.1%, the UK's FTSE 100 and Germany's Dax lost about 2.5%.
Spanish bond yields hit a new high for this year as concerns have returned about Madrid's ability to repay its debts.
Banks were hit particularly hard, with Societe Generale down 6.2% and BNP Paribas 5.7% lower in French trading. In the UK, Barclays fell 5.9% while Lloyds lost 5%.
In Germany, Commerzbank ended the day down 5.9%.
Italian shares fell 5% on media reports the government was about to cut its growth forecast for this year.
And oil declined too. Brent crude fell $2.80 to just under $120 a barrel in London.
Figures released on Friday by the US Labor Department showed the smallest growth in employment in five months.
The US economy added 120,000 jobs during March, less than the 200,000 widely predicted by analysts.
Investors in Europe were given their first chance after the Easter break to react to Friday's disappointing US jobs data.
The figures raised fears about the strength of the recovery in the US economy.
"Opening losses for European stock markets this morning are suggestive of the heavy, negative overhang from last Friday's disappointing US payrolls report," said Jane Foley at Rabobank International.
Meanwhile, the interest rate on Spanish bonds traded in the secondary market continued to rise.
The yield on 10-year bonds hit 5.99%, up from 5.74% on Monday, indicating that investors are getting increasingly concerned about Spain's ability to repay its debts.
"They've managed to put a Band-Aid on the debt crisis, but there's really no solution," said investment portfolio manager Colleen Supran. "And Spain is a much bigger problem than Greece."
Spain makes up about 11% of the total output of the 17 countries that use the euro, while Greece accounts for 2%.
The Iberian nation has introduced a raft of tough austerity measures in recent weeks, partly in an attempt to calm investors' nerves and bring yields down.
Yields are now at their highest level since the beginning of this year, but are still below the 7% considered by markets to be unsustainable.
Also on Tuesday, the head of Spain's central bank, Miguel Angel Fernandez Ordonez, suggested the banking sector may need further support if the economy deteriorates.
"If the Spanish economy finally recovers, what has been done will be enough, but if the economy worsens more than expected, it will be necessary to continue increasing and improving capital as necessary in order to have solid entities," he said.
Investors in Europe also had an eye on Chinese data showing a rise in exports but a sharp fall in imports, while a report from the Organisation for Economic Co-operation and Development (OECD) also gave mixed messages.
It identified a "potential turning point in economic activity in the euro area and regained momentum in other major economies", particularly the US and Japan.
But the report also talked of "diverging" economies in Europe, with Germany and the UK showing a "positive change in momentum" but France and Italy displaying "continued sluggish activity".
Analysts noted general caution ahead of the first quarter reporting season in the US, beginning later on Tuesday with aluminium giant Alcoa.