The euro and dollar both climbed to session peaks against the Swiss franc on Tuesday in volatile trading after a cut in Italy's credit rating late on Monday, although investors said the single currency looked vulnerable on further signs the bloc's debt crisis is worsening.

The dollar was last up 0.7 percent against the Swiss franc at 0.8882 Swiss francs on electronic trading platform EBS, after going as high as 0.8889 francs.

The euro was up 0.8 percent against the Swiss franc at 1.2165 Swiss francs on EBS in early morning New York trade after going as high as 1.2178 francs. The SNB has said it will not tolerate the euro falling below 1.2000 Swiss francs.

The euro had erased gains against the dollar but then rallied and was last up 0.3 percent at 1.37236 on EBS. The session peak posted at $1.3745.