Their lawsuit alleges that the joint federal-provincial environmental review panel did not do its work.
Todd Russell, the president of the NunatuKavut council, claimed the panel did not take into account the accumulative impacts of the Muskrat Falls project, nor did it assess possible energy alternatives.
"So this was not a maybe or discretionary item of business that the panel was supposed to undertake, it was something that they were mandated to take. And they, meaning the joint review panel, by their own admission, did not do it," he said.
"They left work undone, and that is not acceptable."
Russell said they're seeking a court order which would put the brakes on Muskrat Falls.
The order would demand that the panel complete its environmental assessment of the project, and in the meantime, Ottawa would have to stop issuing work permits, and would not be able to move forward with the federal loan guarantee until the assessment is complete.
"This $7.4-billion project has not gone through any real public scrutiny at all, and as a Canadian, and as an aboriginal Canadian, we depend on independent processes to protect our rights, to provide us some security, particularly when we're at odds with the federal government or the provincial government on an issue so fundamental as this," he said.
Natural Resources Minister Jerome Kennedy was unimpressed with comments that a Sierra Club representative made on Monday.
"When I hear our government referred to... as fascists and crooked, I mean I have no reason to give validity to that kind of commentary or that kind of person making the commentary," he said.
"I mean, this is the same group who were sued for libel and backed down."
Kennedy said government will abide by any decision delivered by the Federal Court.