Spanish Prime Minister Mariano Rajoy has said Spain cannot afford to finance itself for long at current rates.Spanish 10-year government bonds have been trading at yields above 6.8%, coming close to the 7% considered unaffordable.
Mr Rajoy was speaking ahead of this week's European Union (EU) summit.
"The most urgent subject is the subject of financing," he said. Spain has asked for funding for its banks, but the country has not been bailed out.
Eurozone countries have agreed to lend up to 100bn euros ($125bn; £80bn) to support Spain's banks.
The yield on government bonds trading on the markets is taken as an indication of the interest rates that governments would have to pay to borrow money.
Mr Rajoy told the Spanish parliament: "There are institutions and also financial entities that cannot access the markets.
"It is happening in Spain, it is happening in Italy and it is happening in other countries," he said.
Separately, there was bad news from the Bank of Spain, which said that the country's recession had probably deepened in the second quarter of the year.The country's economy contracted by 0.3% in the last three months of 2011 and another 0.3% in the first three months of 2012.
The Bank of Spain said its latest data suggested further contraction in the second quarter "at a more intense pace".
On Tuesday, EU authorities put forward their vision for the future of monetary union, which they hoped would reassure investors that they could safely lend to eurozone countries, and avoid further bailouts being needed.
The big dispute in the eurozone is whether bonds will ever be issued jointly by all of its members in order to keep borrowing costs down for those currently facing unaffordable debt.
Tuesday's release from the EU said that could be part of its 10-year plan involving closer fiscal union.
But German chancellor Angela Merkel seemed to dismiss that, reportedly saying: "I don't see total debt liability as long as I live", having already said that the idea of eurobonds was "economically wrong and counterproductive".
Italy held a bond auction on Wednesday, selling 9bn euros of six-month bonds with an interest rate of 2.96%, up from the 2.10% it paid at the last comparable auction at the end of May.Italian Prime Minister Mario Monti and French President Francois Hollande would like eurozone bailout funds to buy government bonds at cheaper rates to help lower the cost of borrowing for indebted eurozone governments such as Spain and Italy on the commercial markets.
In Rome on Tuesday, Mr Monti warned that the EU summit, which is scheduled to take place on Thursday and Friday, could go on into late Sunday if he did not get what he wanted.
But, as the BBC's economics editor Stephanie Flanders points out, the two rescue funds, EFSF and the ESM do not have enough funds to be able to make a serious impact on Spanish and Italian borrowing costs.
For this to work, Germany needs to be willing to allow the ESM to obtain a banking licence, so it can borrow much larger amounts from the European Central Bank, something Chancellor Angela Merkel rejected at last year's July summit.
Cyprus 'not for sale' Also on Wednesday, Cypriot President Demetris Christofias assembled Cypriot political leaders to discuss the country's bailout, which he has told eurozone authorities he will be requesting.
As he emerged from the talks, a journalist told him: "I heard that the island is for sale."
But Mr Christofias replied: "Cyprus island is not for sale and the Cypriot people have dignity and don't challenge me with such questions."
His finance minister said reports that Cyprus would ask for a 10bn euro bailout were speculation.