Spain's cost of borrowing is over 7%, unsustainable in the long term, while Italy's cost of borrowing is over 6%.
Spain's cost of borrowing was 7.016 at lunchtime while Italy's 10-year-bond yield was 6.042.
The main reference interest rate in the euro zone, the Euribor three-month rate, fell to a record low level of 0.549%.
The rate fell sharply from 0.641% yesterday and reflects the terms on which European banks are prepared to lend funds to each other.
It has fallen steadily since the ECB began refinancing banks for up to three years at the end of December.
Euro zone officials are cautioning against expecting any quick action from the currency bloc's finance ministers when they meet on Monday.
Banking supervision, the use of European Union bailout money, aid to Spain and Cyprus and how to deal with Greece all remain to be addressed.
Leaders from the 17 nations sharing the euro reached a deal in the early hours of last Friday to give the European Central Bank greater oversight of the bloc's banks and to use the euro zone's rescue funds to reduce countries' borrowing costs.
But after going beyond what many diplomats, finance officials and investors had expected, critical elements were left vague. Time-frames may already be slipping and opposition is building in euro zone hardliners the Netherlands and Finland.
"You have a Finnish problem. You have a Dutch problem. You have a German problem too," said one euro zone diplomat, pointing to the reservations of those countries about what was announced at the summit and German Chancellor Angela Merkel's reluctance to help its partners without strict conditions.
"I don't see a package done by Monday. They will work until the end of July or the beginning of August on these things," said the diplomat, who is involved in preparations for the Eurogroup meeting of euro zone finance ministers.
Elsewhere, Finnish Finance Minister Jutta Urpilainen said in a newspaper interview that Finland would consider leaving the euro zone rather than paying the debts of other countries in the currency bloc.
"Finland is committed to being a member of the euro zone, and we think that the euro is useful for Finland," Urpilainen told financial daily Kauppalehti, adding though that "Finland will not hang itself to the euro at any cost and we are prepared for all scenarios."
Financially troubled Cyprus, which this week took over the EU presidency, complained of falling "unfairly" foul to Europe's debt crisis and urged euro zone nations to share debt according to size.
Russia confirmed that it had received a €5 billion loan request from Cyprus. "We have received the request. We are currently studying it," the RIA Novosti news agency quoted Finance Minister Anton Siluanov as saying.
Speaking days after applying for an EU-IMF bailout, Finance Minister Vassos Shiarly complained that his tiny island nation went into the red only after paying "a very heavy price" to enable Greece to write off more than €100 billion of debt owed to private banks.
Because Cypriot banks held massive amounts, Cyprus lost 4.2 billion euros, amounting to 24 percent of its gross national product, Shiarly said.
France made a small improvement on its trade deficit in May, but the deficit remains high and a major concern of the government.
The deficit fell by €500m in the month from the level in April to €5.325 billion, the customs service said.
The cumulative deficit over the 12 months to May was €67.559 billion. For the whole of 2011 the deficit was €70.799 billion.
"The figures today confirm the very poor state of our external trade, which began 10 years ago," Trade Minister Nicole Bricq said in a statement.
