The franc has largely traded in tandem with the euro since the Swiss National Bank set a cap of 1.20 per euro last September as investors fleeing the single currency pushed the safe-haven unit up 20 percent in just a few months.
On Monday, 10-year Spanish bond yields jumped as high as 7.596 percent, the highest since the euro was created in 1999. That saw the euro drop for a fourth straight day against the dollar to hit $1.2067, the weakest since June 2010.
The franc was steady against the dollar from the New York close to trade at 0.9914 by 0654 GMT, off a new 19-month low hit on Monday as the currency eyed parity with the greenback.
Alpari market analyst Craig Erlam said there was now significant support around 0.99 after the pair ending above that level on Monday.
"We have already seen the pair bounce off the top of the wedge this morning, confirming it as a new support. This should prompt a move higher with the next resistance level around 1.00," he said.
The franc was steady against the euro at 1.2008.
The amount of cash commercial banks hold with the SNB jumped again last week to 261.6 billion Swiss francs ($263.94 billion)from 249.3 billion, data showed on Monday, a sign the SNB is still having to intervene to defend the 1.20 level.
"Compared to a weekly increase of around 4 billion francs this is a quite marked increase suggesting that the SNB remains engaged in protecting the lower boundary in EURCHF at 1.20 after all," said UBS economist Reto Huenerwadel.