Italy has collected only around 2 billion euros ($2 billion) from a contested windfall tax on energy companies, leaving the Treasury facing a potential multi-billion revenue shortfall, two government sources told Reuters on Friday.

Prime Minister Mario Draghi has budgeted 52 billion euros since January to help firms and households facing sky-high electricity, gas and petrol costs, as the Ukraine crisis weighed on growth prospects for the euro zone's third largest economy.

Between 10 and 11 billion euros of the total package was originally expected to be funded through a 25% windfall tax on energy groups that have benefited from surging oil and gas prices.

Under the scheme, a 40% down-payment worth more than 4 billion euros was from companies due by the end of June.

But thousands of companies refused to pay and some of them publicly complained about the levy, saying that volatile energy prices were also creating problems for their businesses.

In response, Draghi last month approved a measure establishing that the down-payment would carry a 30% surcharge if paid by Aug. 31, after which it would rise to 60%.

Despite the deadlines, the Treasury estimated it had raised less than 1 billion euros by end-June and only an additional 1 billion by Aug. 31, the sources said.

Almost 30% of what has been raised comes from state controlled group Eni, which complied with the scheme paying so far around 560 million euros.

However, the revenue shortfall has no impact on Italy's public finance targets at present, as rising consumer prices and energy costs are lifting indirect taxes such as its VAT sales tax.

What has been collected in August from the windfall tax is part of a 6.2 billion euro of extra support unveiled on Thursday. Rome plans to use the resources to help fund a new relief package worth up to 13 billion euros.

The Treasury is also studying some changes to the windfall tax aimed at reducing litigation risks, as several energy companies are filing appeals, the sources said. ($1 = 0.9907 euros) (Reporting by Giuseppe Fonte in Rome, additional reporting by Francesca Landini in Milan Editing by Keith Weir)