Moody's cut the ratings citing the government's inability to come to the banks' rescue, if that would be needed.
The banks also faced "adverse operating conditions," the rating service said.
The Daily Telegraph reported Friday that yields on benchmark 10-year government bonds in Madrid rose to 6.21 percent, while government borrowing costs fell in Germany and the United States.
British debt was deluged with demand at a $2.6 billion bond auction, the newspaper said.
The flight to safer bonds came as investor service Fitch cut Greece's credit rating from B minus, which is already in junk status, to CCC with "heightened risk that [it] may not be able to sustain membership of the monetary union," Fitch said.
Stock markets in Europe turned lower on the news, with the FTSE 100 index in London hitting a six-month low at 5,338 points, the Telegraph said.
Markets were also lower in Germany and France.
In New York, markets traded on narrow margins, with the Dow Jones industrial average and the Nasdaq composite index both off less than 0.05 percent and the Standard & Poor's 500 up less than 0.2 percent.