The Ibex market fell by 3% and bond yields rose above 6%, a level seen as unsustainable.
On Friday, Madrid will unveil a plan to clean up banks exposed to the property and construction sector crashes.
Much focus will be on Bankia, which holds 32bn euros in distressed property assets and whose boss has resigned.
Rodrigo Rato, who stepped down as Bankia's executive chairman on Monday, was a former head of the International Monetary Fund.
Last month, it was confirmed that the Spanish economy was in recession.
Concern over the weakness of the economy and the deficit have driven up the cost of borrowing for Spain, raising fears it will need a bailout.
That worry has been heightened by the realisation that there is a multi-billion funding gap in the Spanish financial system linked to the 2008 property crash.
Lenders are trying to write down 54bn euros of losses on bad property investments and will struggle to find the extra funds without state assistance.
The current Spanish government, elected in December, has so far insisted that no public money would be used to rescue banks.
But Prime Minister Mariano Rajoy conceded on Monday that "if it were necessary to prompt lending", he would do so "as a last resort".
"The banking issue has been allowed to fester for three years. More public cash will raise funding costs for the government, but it's worth the risk," said Gilles Moec, an analyst at Deutsche Bank.
Bankia has the industry's biggest exposure to the property market.
Spain's fourth-biggest, it was only created in 2010 from a merger of seven struggling savings banks.