The proceeding is Asia's first such climate-related litigation, the plaintiffs said, which includes four petitions by children and infants among others dating from 2020, as well as one from a foetus at the time, nicknamed Woodpecker.
Climate lawsuits are a global trend, drawing increasing public interest, said Lee Jongseok, the president of the court, which is one of the highest in South Korea.
"The court recognises the importance and public interest of this case and will make efforts to ensure that deliberations are conducted thoroughly," he said.
The hearing comes weeks after Europe's top human rights court ruled that the Swiss government had violated its citizens' rights by not doing enough to combat climate change, while courts in Australia, Brazil and Peru weigh similar cases.
"South Korea's current climate plans are not sufficient to keep the temperature increase within 1.5 degrees Celsius, thus violating the state's obligation to protect fundamental rights," the plaintiffs said in a statement.
Scientists say a global temperature rise beyond 1.5 C, or 2.7 degrees Fahrenheit, above the preindustrial average, will trigger catastrophic and irreversible impacts, from melting ice sheets to the collapse of ocean currents.
Burning of fossil fuels, and the resulting carbon emissions, have been linked to rising temperatures, and South Korea's economy relies heavily on such fuels for growth. It has sought to reach carbon neutrality by 2050.
Lawyers for the government told the court the authorities were doing everything possible to cut carbon emissions and not violate the basic rights of its people.
They added that the government did not discriminate against young people, and there could be adjustments to annual goals on carbon reduction.
Several activists said the government's response was unsatisfactory, however.
Dozens of young people, including Woodpecker, who is now a year old, gathered outside the court, with some airing criticism of what they called the government's inaction on climate change.
"Carbon emission reduction keeps getting pushed back as if it is homework that can be done later," said Woodpecker's mother, Lee Donghyun. "But that burden will be what our children have to bear eventually."
The mother of one eight-year-old plaintiff said her children lived in constant fear.
"Because there's a mountain behind our house, the kids say our house can get hit by a landslide. And who knows? That can happen," said Namkung Sujin.
Last year, South Korea revised down its 2030 targets for greenhouse gas reductions in the industrial sector but kept its national goal of cutting emissions by 40% of 2018 levels, describing the move as a reasonable change.