Shortly after the start of trading at 0600 GMT the yield on the benchmark 10-year bonds for Spain rose to 2.720 percent compared with 2.150 percent at close on Friday, while Italy's rose to 2.598 percent, compared with 2.110 percent at close on Friday.
Greece shut its banks and imposed capital controls in a move designed to avert the collapse of its financial system after a weekend of turmoil.
The turbulence is in contrast to last week, when Spanish securities advanced amid optimism a deal would be reached.
Saturday saw the shock announcement by the left-wing Greek Prime Minister Alexis Tspiras to call a referendum on Greece's creditors' austerity measures, in the most dramatic twist yet in five-month negotiations between Greece and its lenders.
But on Monday Spanish Economy Minister Luis de Guindos said he expects Greece will be able to reach an agreement with its bailout creditors before Tuesday night when its existing aid programme ends.
"There is still time, Greece's second programme expires on Tuesday night, which means we still have 48 hours and I think negotiations can still take place," he told public radio RNE.
"I don't exclude that there could be an agreement between now and this deadline, that is at midnight on Tuesday," he added.
Greek authorities ordered Athens' stock market to remain closed Monday, alongside a decision to shut the country's banks for a week and impose capital controls.
The drastic measures to protect Greece's banking system against the threat of mass panic came after the European Central Bank said it would not increase its financial support to Greek lenders, despite early signs of a chaotic bank run.
Spain was battered by the global financial crisis and only emerged from a double-dip recession at the end of 2013.
Its economy has grown for the past seven quarters although the jobless rate remains high at 23.8 percent, the highest in the European Union after that of Greece.
De Guindos, one of the frontrunners to take over the presidency of the Eurogroup of finance ministers this year, said the economic situation in Greece and Spain were not comparable.
"The situation in Spain is very different," he said. "The situation of our banks has nothing to do with what it was three years ago, the same goes for our fiscal deficit," the minister said, before adding that "Spain is well prepared."