The Committee on Climate Change (CCC) says fracking can go ahead if three key tests are met.
And the government says it already plans to meet those tests – on methane leaks, gas consumption and carbon budgets.
Environmentalists argue fracking will make the UK’s climate change targets impossible to achieve.
But the CCC disagrees. Its tests of government policy are:
Though the government is confident these conditions will be reached, a spokesman admitted that any increase in current carbon emissions in future would make current targets even more challenging.
There is already a growing mismatch between the government's long-term promises on climate change and the policies to deliver carbon cuts according to the CCC and National Grid.
There is huge uncertainty about the projections on fracking from the CCC and the government.
The UK currently has no shale gas production, and many observers believe the potential of fracking in the UK has been hyped.
A CCC scenario projecting the most aggressive trajectory of shale gas development with minimum necessary regulation by 2030 estimates emissions of around 11 million tonnes of CO2 a year.
But even that is only a quarter of the UK's emissions from agriculture and land use change. One expert told BBC News: "This is more or less loose change when it comes to the carbon budgets. It’s likely that the local effects like lorry disturbance will prove a more significant issue."
The CCC mostly accepts the government’s reassurances on its three tests. The government is confident it has learned from regulatory failures in the early days of so-called wildcat fracking in the US.
Professor Jim Skea from the committee says with best practice, UK shale gas may have a lower carbon footprint than much of the gas currently imported, which has to be compressed at great energy cost.
But he wants more detail on rules over the completion of wells, when methane can burp out along with the fracking fluid injected into the ground to release the gas. He also wants chapter and verse on how wells will be inspected after they have been decommissioned and before they are abandoned.
He told BBC News: "The CCC accepts that the government plans are mostly on track but wants more detail. Our recommendation is to monitor what government does because we are making the assumption that we have a very well regulated industry and we need some details filled in on that."
The CCC also urged the government to make progress on capture and storage technology, which allows fossil fuels to be burned with minimal emissions of CO2.
The Prime Minister previously said this was vital for the UK before he scrapped a competition to develop it - in order to save cash.
The previous head of the Environment Agency, Chris Smith, said fracking should only go ahead if CCS was imposed, and the CCC report says that without CCS the UK would need to eliminate almost all CO2 from all sectors of the economy by 2050.
A government spokesman said ministers were working on other ways of encouraging CCS without a publicly-funded competition. He also confirmed that the government still intended to show by the end of the year how it would achieve long-term CO2 targets.
The government is to make a final decision on whether to allow fracking at two sites in Lancashire by 6 October.
Energy firm Cuadrilla is appealing against Lancashire County Council's refusal to let it extract shale gas at Little Plumpton and Roseacre Wood.
Professor Richard Davies from  Newcastle University, said: “To do what the Committee on Climate Change recommend, and do it transparently, could force the UK to develop the world’s best ‘smart’ monitoring technologies for emissions from well sites.  There will be new business opportunities if a shale industry takes off."
Dr Doug Parr, chief scientist at Greenpeace, said: "The idea that fracking can be squared with the UK's climate targets is based on a tower of assumptions, caveats, and conditions on which there is zero certainty of delivery.
"The problem with ramping up a whole new high-carbon infrastructure and the fossil fuel vested interests to go with it is that you can't just dial it down later on if emissions start going through the roof."
Labour's Barry Gardiner said: "The CCC report lays out three fundamental tests but the government has decided to do precisely nothing to increase protection for the public or to deliver security for our climate targets.
"On this basis, it is currently neither safe nor reasonable to approve any fracking in Britain."
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The government’s climate change advisors have given a cautious green light to fracking in the UK.