They want the British government to abolish development of the Rosebank site, believed to be the UK’s largest undeveloped oil and gas field.
Ms Thunberg urged ministers to be on the “right side of history” as she protested outside the offices of UK Energy Security Secretary Grant Shapps.
He is expected to decide soon on whether to approve the development, 130km north-west of the Shetland Isles, and believed to be capable of producing up to 500 million barrels of oil.
“The fact that the UK government is even considering this tells us exactly how out of touch with reality they are,” Ms Thunberg said.
“All the record-breaking heatwaves and the extreme weather events we’ve seen during the summer is just the beginning of a rapidly escalating existential crisis.
“We will be seeing much more of this. This is not the new normal – it will continue to escalate and get worse until we start to take real action. And that’s why we need to do it now before it gets even worse.”
It comes amid concerns from climate campaigners that Prime Minister Rishi Sunak is considering watering down some of his government’s environmental policies.
The party’s sole success in three July by elections was when they won Uxbridge and South Ruislip running on a campaign against expansion into the constituency of London’s ultra-low emissions zone by Labour Mayor Sadiq Khan.
After the July by election, their majority was only 495, down from 7,210 for the seat’s departing MP, former prime minister Boris Johnson.
But some right-wing Tories have used the win to urge Mr Sunak to rethink the UK’s net-zero commitments.
Mr Sunak has said he wants a “proportionate and pragmatic” approach to achieving net zero amid cost-of-living pressures.
Ms Thunberg warned that any such approach would be foolhardy.
“To believe that you can focus on one crisis without also addressing the other is so very short-sighted thinking,” she said.
“We seem to be physically incapable of having more than one thought in our head at the same time right now. And that’s very, very dangerous.
“You have to be on the right side of history. We are many who are judging you and who are watching you.
“If you think that you can just get away with a few more years, a few more months of continued business as usual to maximise short-term profits, then you are very wrong and history will judge you very poorly.”