The demands are not the biggest sticking point in attempts to prevent a Greek default by a June 30 deadline. But they have met resistance in Athens, with the privatisation absent from its counter-proposal to creditors.

Among Greece's many economic problems, fuel bills for consumers have been rising and about a third of households have been failing to pay them, EU figures show.

EU regulators say the way to manage energy costs, as well as to improve security of supply, is to implement rules to complete the single EU energy market, break down dominant market positions and share supplies across borders.

A document drawn up by Greece's creditors -- the European Commission, the European Central Bank and the International Monetary Fund -- demands "irreversible steps" towards the privatisation of Greece's electricity transmission company ADMIE, according to a copy seen by Reuters.

ADMIE is owned by Greece's main electricity utility Public Power Corporation (PPC), which is 51-percent state owned.

Greece's previous conservative-led government had planned to carry out privatisations in line EU demands, but the left-wing government of Alexis Tsipras halted the process.

The PPC (>> Public Power Corporation SA) had launched a tender to sell a 66 percent stake in ADMIE, and several investors including state Grid Corporation of China (SGCC) and Italian grid operator Terna were short-listed.

But Terna (>> Terna - Rete Elettrica Nazionale SpA) said in May it had put its plans to buy Greek grid assets on ice because of the uncertainty of the situation.

Greece has one of the worst records on enforcing EU energy law, EU officials say.

Other chunks of EU law that Athens has yet to implement fully include rules on reducing energy use.

EU regulators are also demanding it strengthens the financial and operational independence of its electricity regulator.

Greek electricity tariffs are close to the EU average, but gas tariffs are among the highest in the EU because of a lack of infrastructure and limited number of suppliers, analysts say.

According to Eurostat, the EU statistics office, electricity prices in Greece rose by 5.2 percent between the second half of 2013 and the second half of 2014, the fourth steepest rise in the bloc after France, Luxembourg and Ireland.

European Climate and Energy Commissioner Miguel Arias Canete said in May the reason Greek consumers were facing bigger bills was because of a lack of competition.

(Additional reporting by Stephen Jewkes in Milan; Editing by Philip Blenkinsop and Mark Potter)

By Barbara Lewis