Italian and Spanish 10-year bond yields have been rising ahead of a summit of eurozone finance ministers on Monday.
The yield on Spanish 10-year bonds, which are taken as a strong indicator of the interest rate the government would have to pay to borrow money, rose above 7%, while Italian bond yields rose to 6.1%.
Yields above 7% are considered to be unsustainable in the long term.
Details of the bailout of Spain’s banks are expected from eurozone ministers.
Their meeting will continue on Tuesday.
The high yields on Spanish and Italian bonds were in contrast to the rates at a short-term German bond auction on Monday.
The yield on six-month German bonds fell to a record low of -0.03%, meaning that investors were paying the German government to lend money to them.
It is the second time that German bond yields have been negative. The auction was oversubscribed, despite the negative yield.
Investors have been flocking to German debt as a safe haven from the problems elsewhere in the eurozone.
Eurozone officials have been reported as warning that not too many quick decisions should be expected from the finance ministers’ meeting, which is supposed to add detail to the agreements from the eurozone leaders’ summit on 29 June.
The communiqué from that summit said it expected the finance ministers “to implement these decisions by 9 July”, although many analysts say that now looks optimistic.
Leaders have already agreed to lend Spain’s banks up to 100 billion Euros ($123 billion) and independent audits have said that they will need up to 62 billion Euros.
The finance ministers are likely to confirm the size of the bailout and which conditions will be applied to the loans, both for the banks and the government.
Among the key agreements from the 29 June summit were moves towards banking union with the European Central Bank (ECB) acting as a supervisor and allowing European bailout funds to buy bonds to try to reduce countries’ borrowing costs.
But since the summit, there have been signs that Finland and the Netherlands would oppose the use of bailout funds in this way.
There is expected to be discussion of the new Greek government’s policies. At the end of a three-day debate, the Greek government, as expected, won a vote of confidence on Sunday.
Another area of discussion for the eurozone finance ministers will be choosing a new leader.
Jean-Claude Juncker has been co-ordinating the Eurogroup of finance ministers since 2005. His term of office ends on 17 July, but it may be extended.
Also on Monday, ECB president Mario Draghi will be appearing before the European Parliament’s Committee on Economic and Monetary Affairs to give his views on the state of the currency bloc’s economy.