Greenpeace, along with environmentalist youth group Natur og Ungdom (Nature and Youth), has sued the Norwegian state over licences it awarded in 2016 for oil prospecting in the Barents Sea.
The Scandinavian country is western Europe's biggest oil producer.
A third group, called the Grandparents Climate Campaign, has also joined the case against the state.
The plaintiffs accuse Norway of violating the Paris Agreement on climate change and a section of the country's constitution amended in 2014 that guarantees the right to a healthy environment.
A lawyer for the plaintiffs, Cathrine Hambro, asked the court in her opening remarks to determine whether the decision to carry out oil prospecting was "within the existing guidelines for decisions that can have irreversible consequences," news agency NTB reported.
The organisations claim their lawsuit was the first to be filed against a state for violating the agreements signed at the COP21 climate change conference in Paris in December 2015, which came into force in November last year.
"It is clear to us that this new search for oil is in violation of the Paris Agreement and the Norwegian constitution, and we look forward to raising these arguments in court," the head of Greenpeace Norway, Truls Gulowsen, said in a statement on the eve of the first court day.
Norway's oil revenues are dwindling, with crude oil production now half what it was in 2001.
In May 2016, it awarded 10 licences covering a total of 40 blocs to 13 oil companies, including Norway's state-owned mammoth Statoil, US groups Chevron and ConocoPhillips, Germany's DEA, Japan's Idemitsu, Sweden's Lundin, OMV of Austria and Russia's Lukoil.
The NGOs are now calling for the concessions to be cancelled because of the environmental risks.
Norway has insisted it is abiding by the constitution and the "validity of the licences cannot therefore be attacked on this basis," energy ministry spokesman Ole Berthelsen has said.
Three of the most contested licences are located in the immediate vicinity of a maritime border with Russia that has remained unexplored until now, in an area that the two countries long disputed before reaching an agreement in 2010.
One of these zones is the northernmost Norway has ever opened to prospecting, and the NGOs are concerned about its proximity to the ice floes.
"The Norwegian government, like every government, has an obligation to protect people's right to a healthy environment," Ingrid Skjoldvær, a spokesperson for Natur og Ungdom, said in a statement.
With drilling in the Arctic, "it is us in the younger generation, and our children, who will feel the worst effects of this oil being burned."
Paradoxically, Norway is home to the world's biggest fleet of electric cars per capita. It aims to end sales of new cars equipped with only combustion engines by 2025.
But Norway's black gold has also enabled it to build up the world's biggest sovereign wealth fund, today worth around $1.0 trillion.
In June, Norway proposed opening up oil exploration in a record number of blocs in the Arctic waters of the Barents Sea, despite opposition by environmentalists and some parts of its own administration.
Of the blocs the oil and energy ministry put on offer, 93 are located in the Barents Sea and nine others in the Norwegian Sea, also above the Arctic circle.
The Nordic country was one of the first to ratify the Paris Agreement, which seeks to limit average global warming caused by greenhouse gases from fossil-fuel burning to under two degrees Celsius (3.6 degrees Fahrenheit) over pre-industrial levels, and to 1.5 C if possible.
But the oil industry considers the waters opened to prospecting, especially those close to Russia -- ice-free thanks to the Gulf Stream -- to be promising, crucial for Norway at a time when its oil production has been in constant decline since peaking in 2000.
The case is being watched closely around the world.
"What happens in Norway in this case will have an effect on how these issues are considered elsewhere," University of Oslo law professor Ole Kristian Fauchald told Norwegian public broadcaster NRK.
"A decision in the environmentalists' favour will be noticed and will set an important precedent. So there's a lot at stake."
The court case is expected to continue until November 23rd.