Spanish and Italian 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 summit of eurozone leaders on 29 June said it expected the finance ministers “to implement these decisions by 9 July”.
Leaders have already agreed to lend Spain’s banks up to 100bn euros ($123bn; £79bn) and independent audits have said that they will need up to 62bn euros.
The finance ministers are also likely to confirm which conditions will be applied to the loans, both for the banks and the government.
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Analysis
image of Chris Morris Chris Morris Europe correspondent, BBC News
Splits are emerging between southern and northern members of the eurozone about how to implement decisions taken at a European summit last month.
Tempers within the single currency area appear to be fraying.
Spain and Italy want agreements made at the summit to be put into effect as soon as possible, making it easier to use eurozone bailout funds to help struggling banks or struggling countries.
But other member states, notably Finland and the Netherlands, have said they’re not going to be pushed too quickly into any kind of collective responsibility for other countries’ debts.
Finance ministers will have to find a way around this impasse.
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.
Source bbc.