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 ...view middle of the document...
It adds that further research is needed to ensure the change would not make it more difficult for police to access information about calls and emails that is "crucial to keeping us safe".
The Labour Party has seized on the apparent clash.
"The detail of this policy needs careful consideration," said Harriet Harman, shadow culture secretary.
"Rather than briefing against each other as part of the ongoing Tory leadership squabble to replace David Cameron, cabinet ministers should be making clear what the impact will be on 4G services for consumers and the emergency services, as well as any possible implications for national security and the fight against serious crime."
BBC technology correspondent Rory Cellan-Jones said mobile phone operators had indicated that national roaming would be bad for the consumer.
"Operators argue that roaming would shorten battery life as phones searched for the strongest signal, and pose a risk to the security of their networks," he said.
He said the operators wanted changes to planning laws and the ability to build and share more phone masts.
Matthew Howett, an analyst with research firm Ovum, also thinks that the government's preferred plan of national roaming is "a messy solution that ought to be abandoned".
"The cost, complexity and side-effects of national roaming make it such an unworkable fix that the industry thought had been dropped," he told the BBC.
"What needs to happen over the next month is collectively for the the mobile operators to work with government to come up with an agreeable fix that addresses not only poor voice coverage, but also data too," he added.
Making it easier for operators to put up masts quickly in a cost-effective way would also help current coverage issues, he added.
Mobile spectrum auctioned last year was well-suited to covering rural areas and operators were starting to make use of it and that too should help improve the situation, he said.
While the government's consultation is looking specifically at 2G services, a study commissioned by consumer watchdog Which indicates 3G and 4G coverage is also patchy around the UK.
The report into the state of the mobile phone network found big differences...