Deputies said they would appeal to the United States and Russia in particular to guard against possible errors in computer systems that cannot recognize the date change to 2000.
U.S. and Russian military officials are due to spend New Year's Eve together in a special command center designed to avoid accidents caused by the millennium bug.
The parliament voted to ask countries with nuclear power stations to shut them down over New Year's Eve unless they had been shown to be millennium compliant.
Deputies said their appeal would be aimed specifically at countries in central and Eastern Europe, Turkey, Russia and members of the former Soviet Union.