Concern remains about eurozone debt, despite the 100bn-euro ($125bn; £80bn) bailout of Spain's banks, as borrowing costs for Italy and Spain both rose.
Ten-year Italian bond yields rose from 5.758% to close at 6.032%. Spanish bond yields were also up, to almost 6.5%,
Meanwhile, ratings agency Fitch downgraded two Spanish banks, Santander and BBVA, two notches from A to BBB+.
Stock markets worldwide had opened higher after the Spanish deal but their initial enthusiasm later faded.
New York's Dow Jones, up 0.7% on opening, finished 1.1% lower. London's FTSE 100 started strongly but closed down 2.7 points. The French and German indexes were little changed.
The Nikkei in Tokyo closed up 2.0%. The Hang Seng in Hong Kong closed up 2.4%.
Oil prices also tumbled on fears that the eurozone debt crisis will engulf more countries and threaten demand for petroleum. US light crude fell $1.40 to $82.70 a barrel, while Brent crude dropped $1.47 to settle at $98 a barrel.
"Markets have found it very difficult to hang on to anything close to the bulk of their gains with sentiment tempered by the realisation that, after looking beyond the headline bailout figure to ask what has really changed beyond that number," said Michael Hewson from CMC Markets.
The rise in Italian and Spanish bond yields is an indication that investors are still worried about the countries' finances.
Fitch said its ratings action on Santander and BBVA was linked to its downgrading of Spain's sovereign credit rating last week.
In particular it cited the forecast that Spain will "remain in recession through the remainder of this year and 2013 compared to the previous expectation that the economy would benefit from a mild recovery in 2013 which directly affects the banks' volumes of activities in Spain".
'Statement of intent'
Spain's weakest banks were left with billions of euros of bad loans following the collapse of a property boom and the subsequent recession.
The exact amount of emergency funding that Spain will receive will be decided after two audits of its banks are completed within the next few days.
Speaking at the European Parliament in Strasbourg, the EU's economic and monetary affairs commissioner Olli Rehn re-iterated that Spain would not have to implement any new austerity measures in return for receiving financial aid.
"Policy conditionality will focus on the financial and banking sector," Mr Rehn said.
"There will be no new conditions on fiscal policy and structural reforms because these issues are dealt with under the reinforced economic governance and there, the normal policy conditionality applies."
Spain is in its second recession in three years and the economy is expected to shrink by 1.7% this year. The longer the downturn lasts, the harder it will be to repair the banks' and country's finances.
"The Spanish announcement is not a solution to the eurozone's ongoing woes, but it is a statement of intent," said Richard Hunter from Hargreaves Lansdown stockbrokers.
"Some much-needed time has now been bought in Spain, which will allow the market an at least temporary sigh of relief."
'Happy or humiliated'
Spanish journalist Miguel-Anxo Murado told BBC News that many Spanish people were surprised there had been a bank bailout at all.
"The government has been very successful at denying the need for this bailout," he said.
"Now the controversy is actually whether we should be happy or humiliated about this."
The government has been keen to stress that it is the banks that have been bailed out, not the country.
But in an interview on Monday, EU competition commissioner Joaquin Almunia said there would be a troika of authorities to oversee the financial assistance, just as happened with Greece, Portugal and the Republic of Ireland.
The troika will be made up of the International Monetary Fund, the European Central Bank and the Eurogroup of eurozone finance ministers.
With loans to the banks set to add to government debt, the agreement reached on Saturday has done little to ease concerns about the country's debt burden.
The Spanish government said in a statement late on Sunday that it was committed to its programme of economic reforms.
The Treasury said it would continue to borrow money commercially and confirmed it would continue with its planned programme of bond auctions.
But with the terms of the bank deal still unclear, investors appear to be still wary of lending to Spain, as indicated by the higher bond yields.
The next bond auctions scheduled are short-term sales on 19 and 21 June, after the Greek elections on 17 June, which will be the next key test for the eurozone.
'A lot to do'
The rise in Italian bond yields suggests that investors are concerned about whether Italy will be the next country to get into difficulties.
But Italy's economic development minister, Corrado Passera, has said that his country has already taken the necessary measures.
"This great discipline that we have imposed on ourselves in terms of public finances makes us one of the countries best equipped to confront the financial turbulence that Europe finds itself in today," he said.
Official figures on Monday confirmed that the Italian economy had contracted by 0.8% in the first three months of 2012.
Mr Passera conceded that Italy still had "a lot to do" to boost growth.