Ami McCarthy, head of politics at Greenpeace UK, said: “Trying to squeeze the last few drops of expensive oil and gas out of the North Sea while the world is reeling from climate impacts is beyond ridiculous.”
But David Whitehouse, chief executive of industry body Offshore Energy UK, said Jackdaw would be “one of the lowest emission fields in the world”.
He told the BBC’s Radio Scotland Breakfast: “I think we all recognise that we have got to deal with emissions.
“But the reality is that, on that journey, we are going to need oil and gas.
“We would argue that while we use oil and gas we should prioritise our own and produce and support our own.”
Whitehouse said one in 30 jobs in Scotland were in the oil and gas industry.
And he told the programme that producing instead of importing oil and gas, from countries such as the US and the United Arab Emirates, “comes with much lower emissions”.
Supporters of further drilling, including the Conservatives and some trade unions have also said it will not make a significant difference to emissions and is vital for protecting jobs.
President Trump has also been a vocal supporter of North Sea drilling, and said Burnham “sounded terrific” on the issue in their first phone call last month.
In that call, Burnham told Trump the UK “can’t ignore” resources in the North Sea, and said he would take “a pragmatic approach” to further drilling.