Fitch ratings agency has said it is considering downgrading six nations that use the euro - Italy, Spain, Ireland, Belgium, Slovenia and Cyprus - by one or two notches.
Following last week's European Union summit, it "has concluded that a 'comprehensive solution' to the eurozone crisis is technically and politically beyond reach".
It expects to complete the review of the countries' ratings by the end of January.
Meanwhile, Moody's Investors Services said it downgraded Belgium's credit rating by two notches, citing strains on eurozone countries as they try to finance their heavy debt loads.
The ratings agency said it cut the nation's local and foreign-currency government bond ratings on Friday to "Aa3" from Aa1", with a negative outlook. The ratings remain investment grade.
Moody's said the downgrade comes as soaring borrowing costs strain the finances of heavily indebted countries that use the euro, such as Belgium.
The strains are also making it difficult for Belgium to reduce debt and rein in spending.
Also being taken into account are increasing risks to Belgium's economic growth and concerns about the small nation's banking sector.