Under the agreement, Deutsche Telekom, Vodafone and Telefonica Deutschland will plug holes in coverage over and above the 98 percent they committed to in the last spectrum licensing round.

Mobile network coverage in Europe's largest economy is often patchy and, together with delays in building out high-speed internet, has been criticised by business groups as a handicap in the digital era.

Scheuer, who represents the Bavarian Christian Social Union in Chancellor Angela Merkel's grand coalition, has been looking for a policy win ahead of a regional election in the large southern state in October.

"We are starting a unique network buildout offensive for Germany," he said after signing a mobile pact with the industry.

The three telecoms operators have, for their part, said the cost of filling in the last gaps on the map is prohibitive and called on the government to adjust the subsidies on offer to make the investments affordable.

In a joint declaration, the companies also committed to ensuring that 99 percent of households have 4G network coverage in each of Germany's 16 federal states during the course of 2021.

This would entail building 1,000 4G masts in areas where there is currently no coverage and upgrading another 10,000 masts.

In turn, Scheuer promised to ease the terms of next year's auctions for fifth-generation mobile services - that could be used in self-driving cars or telemedicine.

As part of this agreement, operators would only have to pay for new 5G spectrum once it is allocated. This, Scheuer said, would save the industry around 1 billion euros (883.51 million pounds).

($1 = 0.8568 euros)

(Reporting by Markus Wacket and Douglas Busvine; Editing by Keith Weir)