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Bye!s\gn\.mwmobile networks, affected a fifth of the UK, leaving people unable to make calls or send texts, it said.
One possible solution would see people transferred to rival networks when they lose signal.
But experts are not convinced this would work.
Culture Secretary Sajid Javid said he was determined to sort out the issue of mobile notspots.
A series of talks held with mobile operators has so far failed to find a solution.
"It can't be right that in a fifth of the UK, people cannot use their phones to make a call. The government isn't prepared to let that situation continue," he said.
The proposals to end the frustration - currently only aimed at improving 2G services - are as follows: * National roaming - phones would use another network when theirs was unavailable, similar to how roaming works when abroad * Infrastructure sharing - mobile networks would be able to put transmitters on each other's masts * Reforming virtual networks - agreements that companies such as Tesco and Virgin currently have with single operators would be extended to all four networks * Coverage obligation - obliging the networks to cover a certain percentage of the UK - and leaving them to decide how to do it
The government has given the industry, businesses and the public until 26 November to respond to the proposals.
Leaked letter
Mr Javid may face opposition to the move from within his own party.
The Times newspaper has reported that a leaked Whitehall letter contains a warning from the Home Secretary Theresa May that allowing people to roam between networks could compromise efforts to track criminals and terrorists.
Mr Javid's plan is reported to have prompted Theresa May to warn of security issues
"[It] could have a detrimental impact on law enforcement, security and intelligence agency access to communications data and lawful intercept,"