Italian prosecutors have launched an inquiry after the worst blackout in the country's history left more than 50 million people without power.
Virtually the whole of Italy was hit
Several areas in Italy were waiting for supplies to be restored early on Monday.
As debate raged over what went wrong, the Rome prosecutor's office said its inquiry would try to establish who was responsible.
Officials were warning of "programmed" cuts on Monday to avoid overloads.
"We are planning precautionary cuts to reduce demand so that it meets the availability (of power)," said Andrea Bollino, chairman of the national grid company GRTN.
August 14 - US and Canada
August 28 - London, UK
September 23 - Denmark, Sweden
September 28 - whole of Italy
Sunday's power loss was the latest in a series of major blackouts to affect national power grids.
Last month a vast section of the United States and Canada lost power, hitting 50 million people.
The incident was followed two weeks later by one in the UK. Last week the Danish capital, Copenhagen, and southern Sweden were hit.
The blackout appears to have been triggered by a minor accident on a power line in neighbouring Switzerland, causing a domino effect in French lines which affected Italy. Parts of the Swiss city of Geneva were also blacked out.
On Monday Switzerland and France were blaming Italy for having failed to take action that would have limited the scale of the problem, while Italy said France was at fault.
Mr Bollino also faced criticism for having reassured the Italian public after the US blackout that the problem could not happen there.
At least five people are reported to have died in accidents during the blackout. An estimated 30,000 were trapped on trains.
Only the island of Sardinia escaped the blackout, which struck at about 0330 (0130GMT) on Sunday morning.
Areas still feeling the effects on Monday included Enna and Caltanissetta on Sicily, and Puglia in the south-east.
The power failure in Italy has highlighted the country's dependence on energy imports.
Thousands of travellers were left stranded
A spokesman for Enel, the Italian utility company, said the country imported up to 17% of its power, compared with a Europe-wide average of 2%.
He said that poor organisation in the Italian grid made the problem worse.
Environmental opposition to building new power plants means that Italy has become more and more dependent on power imports.
Industry Minister Antonio Marzano called for a backing for a bill to increase power output by 12,000MW, a quarter of the current capacity.
The head of the power company echoed his call.
"I would like my fellow citizens to know that we must build new plants and networks on our territory or the
situation will remain the same," said Enel chief executive Paolo Scaroni.
A Swiss power company said the problem began when a tree touched a 380,000 volt transmission line near the town of Brunnen at 0300 (0100GMT).
Atel, a Swiss power supply company, said that two French transmission lines also failed shortly afterwards.
"After that, all connections to Italy dropped out," said an Atel spokesman.
Three elderly women died in separate incidents when they fell downstairs in the dark, a fourth woman died of burns after a candle set her clothes ablaze, and one woman died in a road accident caused by the lack of traffic lights.
At the Vatican, emergency generators were started up to provide power to amplify Pope John Paul II's announcement of a list of new cardinals.