Perhaps more importantly, the yield on Spain's 10-year bond dropped by 0.32 percentage points to 6.58 percent. Italy's was down by 0.14 percentage points to 5.94 percent. Both countries have seen their rates edge toward the 7 percent level which is seen as unsustainable over the long term.
The importance of recapitalizing banks directly from the bailout fund became evident this month when Spain was offered €100 billion ($125.6 billion) for its shaky banks. Previously the bailout loan would have to be made to the Spanish government, which would lend it on to the banks. The prospect of having that debt on the government's books spooked investors, who began demanding higher interest rates to reflect the risk of a Spanish default.
Lending the money directly to the banks avoids putting more debt on the government's books.
Also boosting market confidence was the agreement to waive the permanent bailout fund's preferred creditor status for aid given to Spanish banks. So far, any money the fund puts into a bank would get repaid before any other investors.
When Spain agreed to take rescue loans for its banks, the news failed to boost confidence in the banks because investors worried that, if one of those banks collapsed, they would be last to get repaid. Eurozone leaders agreed to waive the bailout fund's preferred creditor status only in Spain's case.
Some analysts, however, noted that the size of the bailout funds some €500 billion would have to be increased to be a realistic backstop for public debt and banks across the continent. Italy alone has government debt of €2.4 trillion.
"These steps are the obvious ones to take to try to restore some confidence in the market in the short term," said Gary Jenkins, managing director of Swordfish Research in London. "Alone, they do not solve the underlying problems but they might buy a bit of time, which is probably about the best they can do right now."
Though welcoming the measures that were taken, analysts think more will have to be done.
"If the aim is to ease tensions on the Italian and Spanish bond market on a more sustainable basis, we probably will need to have more assurance on the fire power," said analyst Carsten Brzeski of ING in a note.
Brzeski said more liquidity support from the ECB — such as in the form of cheap loans to banks — "looks inevitable" and may come as soon as Monday.
The EU leaders also agreed to devote €120 billion in stimulus to encourage growth and create jobs, though half of it had already been earmarked and it includes only €10 billion in actual new commitments. France had pushed for the growth package, arguing that austerity measures are stifling growth and making debt reduction more difficult.
They also agreed to give the ECB powers to oversee big European banks by the end of the year.
For the longer-term, the 27 leaders of the EU agreed on "four building blocks" of a tighter union — but postponed specifics until a study due in October. The building blocks, which include sharing debt in the form of jointly issued eurobonds, were laid out in a sweeping document presented by Van Rompuy and colleagues before the summit.
However, France's President Francois Hollande said the general agreement on the tighter union did not for now include any commitment on eurobonds from Germany and other stronger economies that have firmly opposed sharing debt with more profligate countries such as Greece.
Hollande claimed to play the role of mediator instead of partnering with Germany as France traditionally does.
"No one can say I won or I lost," he said. "What was at stake was Europe. That's who won."
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