Tassos Kourakis said the bill, which paves the way for a bond swap, which would wipe €107 billion ($142 billion) off the country's privately-held debt, was approved Thursday though no roll call vote was held.
Greece is now expected to issue the formal bond offer, under which private creditors will be called on to exchange the bonds they hold with new ones of lower value and longer maturities.
The bond swap is an integral part of a new bailout for Greece, worth €130 billion ($172 billion), without which the country faced bankruptcy next month.
