Spain's prime minister has said it is "very difficult" for the country to get funds.
He was speaking amid growing fears about the Spanish banking sector, after Bankia asked the government for 19bn euros ($24bn, £15bn).
The premium investors demanded for holding Spain's 10-year bonds over its German equivalent rose to a record 5.05 percentage points.
But Mr Rajoy said the banking system did not need an international bailout.
"There will not be any [European] rescue for the Spanish banking system," he said, but he backed calls for the European rescue fund to be able to lend to banks directly.
Last week Bankia, which was formed from the merger of several struggling regional lenders, requested a 19bn-euro bailout, which was a much bigger amount of help than had been expected.
"We took the bull by the horns because the alternative was collapse," said Prime Minister Mariano Rajoy, adding that Bankia customers' savings were now safer than ever.
It marks an effective nationalisation for the country's third-largest bank and has raised fears about how Spain plans to pay for it.
Rather than borrowing money on the open markets, potentially at high cost, there are reports that Madrid is considering giving Bankia government bonds. The bank would then use them as collateral for loans from the European Central Bank.
One analyst said this would amount to "an ECB bailout through the back door".
Some are concerned that by doing this, the government is not tackling the problem of the huge amount of bad property loans, estimated at 32bn euros, that Bankia is holding.
"It is not dealing with the problem of bad loans, it is just keeping them going," said Kathleen Brooks, research director at Forex.com. "It risks becoming a zombie bank," she told BBC News.
Bankia's shares lost almost a third of their value earlier, in their first trading session since the request for government help. They later closed down 13%.
There were also reports in a Spanish newspaper, El Mundo, that the government may have to inject an additional 30bn euros into three other nationalised banks; CatalunyaCaixa, NovacaixaGalicia and Banco de Valencia.
Mr Rajoy said he did not think his government's support for Bankia had influenced what is known as the risk premium, the difference between Spanish and German bond yields.
"There are major doubts over the eurozone and that makes the risk premium for some countries very high."
"That's why it would be a very good idea to deliver a clear message there's no going back for the euro," Mr Rajoy said.
The higher bond yields rise, the more expensive it is likely to be for governments to borrow money.
Kathleen Brooks said "it seems only a matter of time" until bond investors demanded an even greater rate of return than the record high of 6.7% reached in November 2011.
Elisabeth Afseth, an analyst at Investec, said that rising bond yields in certain parts of the eurozone would make it harder for those countries to straighten out their finances.
"If it goes on for much longer, it just adds to the burden of fiscal consolidation, she said.
"If a large part of that [the yield] is spent on paying a premium to borrow, it just makes it so much harder."
Italian government bond yields also ticked higher, rising to 5.87%.
Despite the worries about Spain, which caused its main share index to close 2% lower, other European stock markets started the day higher.
Greek shares rose 7% after a weekend poll in Greece showed growing support for a pro-austerity conservative party.
The poll suggested the New Democracy party could gain about a quarter of the votes, leaving it as the biggest party, albeit without overall control.
The next elections are scheduled for 17 June.
London, Paris and Frankfurt markets all rose at least 1% at the start of trading, before trimming gains to close flat on the day. Although both Germany and France have a public holiday on Monday, their equity markets remain open.----
In: World News
Tags: spain, euro, zone, crisis, economy, EU, social, unrest, polls, greece, france, italy, germany
Location: Spain (load item map)
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