By Tom Käckenhoff and Christoph Steitz

The deal, part of a bigger asset swap with Innogy's parent RWE which would more than double E.ON's customers in Germany to nearly 14 million, is the subject of a deepened EU investigation into whether it will hurt competition.

Chief Executive Johannes Teyssen said late on Monday that E.ON has offered to sell part of its retail business in Hungary as well as Innogy's retail power and gas business in the Czech Republic, with 1.6 million customers, to ease EU concerns.

E.ON has also offered to drop 260,000 heating customers in Germany, as well as the right to operate 32 charging stations for electric cars along Germany's Autobahn motorway network.

Smaller rival Lichtblick, which has been highly critical of the deal, said the proposals went in the right direction. "However, we take the view that the concessions that were announced for Germany would not be enough," a spokesman said.

As part of the European Commission's antitrust review, to be wrapped up by Sept. 20, customers and rivals have been asked to respond to E.ON's proposals this week as part of a so-called market test to see whether the remedies are sufficient.

"E.ON needs to divest the many participations in municipal and regional utilities in Germany," Tim Meyer, a board member at Naturstrom AG, said. "Only that way you can avoid E.ON simply crushing smaller competitors in the power retail and distribution grid operating businesses."

Innogy's parent RWE and E.ON agreed last year to break up the group and divide its assets between them in the biggest overhaul in the German power industry since Berlin sped up its exit from nuclear after Japan's Fukushima disaster in 2011.

As part of the planned deal, RWE will combine the renewable assets of Innogy and E.ON to become Europe's third-largest player in this sector, behind Spain's Iberdrola and Italy's Enel.

Meanwhile, E.ON will be transformed into one of the continent's biggest networks and retail players by integrating Innogy's grids and customer units.

"Overall, with this newsflow, we believe any significant roadblocks to the E.ON-Innogy merger have been averted with minimal impact," Bernstein analysts said in a note.

(Additional reporting by Foo Yun Chee in Brussels; Writing by Tom Sims; Editing by Jan Harvey and Deepa Babington)

By Tom Käckenhoff and Christoph Steitz