The case is led by Greenpeace Norway and Nature and Youth, and has the support of the Norwegian Grandparents Climate Campaign, and Friends of the Earth Norway.
Frode Pleym, the leader of Greenpeace Norway, told The Local that he was "very happy to be in court again because we think the issue is urgent."
"The Norwegian government must stop pretending that they are a front runner for the climate, because they are not for as long as they don't address the white elephant in the room, which is the oil production."
He said the first day, in which the defence and prosecutor both made their opening statements, followed by statements from Greenpeace and Friends of the Earth, had gone "quite well", and said he was looking forward to Wednesday's session, when experts on climate science and international politics would give evidence.
He said in a press release ahead of the session that the country had both "a legal and a moral responsibility" for the oil it produces.
"We have signed the Paris Agreement and therefore committed to work to keep global warming below 1.5 degrees," he said. "The research shows that even the existing fields take us past this climate target, so we cannot open up new areas for oil drilling."
On the eve of the court appeal, campaigners held a National Action Day, with events at over 20 locations around the country, and candles lit across the country at 18.14pm. According to Greenpeace, 540,000 people have given their support to the case in writing.
The groups' lawyers, led by Cathrine Hambro from the Oslo lawfirm Wahl-Larsen, are expected to argue that allowing drilling in the Arctic violates Section 112 of the Norwegian constitution, which states that citizens have the right to a "liveable environment", and that the government must act to safeguard this right.
The suit concerns ten new exploration licenses awarded in 2016 during the 23rd Norwegian licensing round.
In 2018, the Oslo District Court rejected a similar argument, arguing that the country should only be held responsible for greenhouse gases derived from Norwegian-produced oil and gas if they are emitted in Norway.
The groups aim to contest this at the Borgarting Court of Appeal.
David Boyd, UN special rapporteur on human rights and the environment, last week called for the country to stop future oil and gad exploration.
“Norway should stop exploring for additional oil and gas reserves, stop expanding fossil fuel infrastructure, and harness Norwegian wealth and ingenuity to plan a just transition to a fossil fuel-free economy,” he said.
The appeal will run until Thursday next week, with a possible extra day on Friday. The verdict is expected some time in early January.