The legal action, which has been in the works for two years, comes as Sweden's new right-wing government faces mounting criticism over lacklustre climate goals.
Moa Widmark, a 19-year-old student, said she was taking part in Friday's demonstration because "the climate crisis is worrying and scary -- we're headed for a catastrophe".
While the lawsuit is a first in the Swedish courts, six Portuguese youths have taken Sweden and 32 other countries to the European Court of Human Rights accusing them of failing to adequately address the climate crisis.
"If we win, there will be a verdict that says the Swedish state is required to do its share of the global measures needed for the world to meet the 1.5 degree target", Edling said.
In recent years, a growing number of organisations and citizens have turned to the courts to criticise what they claim is government inaction on the climate.
In December 2019, the Dutch supreme court ordered the government to slash greenhouse gases by at least 25 per cent by 2020, in a landmark case brought by an environmental group.
In a similar case in France, more than two million citizens took the French state to court for failing to act against climate change.
In a report published earlier this week, the Swedish Meteorological and Hydrological Institute said the average temperature in Sweden had risen nearly two degrees Celsius (35.6 degrees Fahrenheit) since the late 1800s, twice as fast as the global average.
Snow cover now lasts two weeks less, while precipitation has increased.