The Hague District Court last year ordered Shell to reduce carbon emissions produced by it, its suppliers and customers by 45% by 2030 from 2019 levels, a landmark decision that could have implications for energy companies around the world.
Shell is appealing against the ruling.
The group Friends of the Earth/Milieudefensie said it sent a letter to the company's boards and individual representatives on Sunday, including CEO Ben van Beurden, saying it was not acting to implement the verdict.
"Shell has appealed, but the court declared the judgment provisionally enforceable, which means the necessary climate action cannot be suspended pending the appeal," the group said in its letter, a copy of which was seen by Reuters.
"Milieudefensie believes that Shell's directors risk future personal liability by failing to take action in line with the ... goal of almost halving worldwide CO2 emissions by 2030."
Shell, which says it is adhering to the court ruling in most respects, said it was reviewing the Mileudefensie letter.
"The court gave Shell a broad discretion as to how to meet the reduction obligation by its 2030 deadline," the company said. "Our strategy and the actions we are taking position us well towards meeting the court’s obligations."
The company did not address the question of whether board members might have personal liability in complying with the ruling.
In its appeal filed in March the company argued that it had wrongly been held responsible for emissions by customers, which it said it cannot control.
Shell's targets include cutting its emissions by more than 50% by 2030, though its strategy includes using carbon storage and offsets rather than outright reductions.