In afternoon Tokyo trade, the euro sank to 121.77 yen from 124.61 yen in late New York trade Friday and to $1.2902 from $1.3075.
The dollar also weakened to 94.36 yen from 95.26 yen.
As a condition for a desperately needed 10-billion-euro rescue, fellow eurozone countries and international creditors at the weekend imposed a levy on all deposits in the island's banks.
Cypriot bank customers have voiced dismay and anger that they alone of the five eurozone member countries forced to seek bailouts so far were being expected to help foot the bill.
But President Nicos Anastasiades said the levy on private depositors was the "least painful" option for the recession-hit island. The Cypriot leader warned that rejecting EU demands would have seen Cyprus exit the 17-nation eurozone and face bankruptcy.
Under the proposal, which must be passed by parliament in Nicosia, deposits of more than 100,000 euros will be hit with a 9.9 percent charge and 6.75 percent for anything below that threshold.
While the Cyprus bailout is relatively small, the "levy could have wide-ranging repercussions on eurozone bank deposits in other peripheral countries, despite Cyprus... being labelled as 'unique'" Credit Agricole said.
A political deadlock in Italy also weighed on euro sentiment with doubts about talks aimed at forming a government, it added.
"There is little to suggest a deal is in the offing with the risk skewed towards protracted negotiations and fresh elections," Credit Agricole said.
Jitters over Europe had investors moving back into the yen, which is considered a safe option during times of uncertainty.
Markets were eyeing a US Federal Reserve meeting for clues about policy moves after a decline in a key US consumer sentiment index highlighted continuing weaknesses in the world's biggest economy.
The yen's gain reversed a decline Friday sparked by Japan's parliament approving a new central bank management team widely expected to usher in more aggressive monetary easing to stoke the world's third-biggest economy.
Governor Haruhiko Kuroda and his two deputies will take up their posts later this week.
The dollar was stronger against other Asia-Pacific currencies.
It rose to Sg$1.2515 from Sg$1.2485 on Friday, to 40.69 Philippine pesos from 40.58 pesos, to 54.29 Indian rupees from 54.06 rupees, to 9,709 Indonesian rupiah from 9,705 rupiah, and to 29.59 Thai baht from 29.57 baht.
The dollar also firmed to Tw$29.75 from Tw$29.72 and to 1,114.46 South Korean won from 1,109.30 won.
The Australian dollar weakened to $1.0359 from $1.0375 while the Chinese yuan fetched 15.21 yen against 15.45 yen.