Describing the sentences of between 15 months and five years as "the highest of their kind in modern British history", lawyer Danny Friedman told London's Court of Appeal that the activists "did what they did out of sacrifice" and were acting in the "best interests of the public, the planet and future generations".
The hearing is being closely watched amid fears that peaceful protest risks being stifled in the UK.
In another case in southwestern England, two other protesters denied charges over a stunt at the prehistoric monument Stonehenge last year.
Climate campaign group Just Stop Oil claimed the 16 protesters appealing against their sentences were "political prisoners".
"They are not there because they disrupted or harmed everyday people... No, they are there because Just Stop Oil threatens the profits of the fossil fuel industry," said the group.
- Soup, orange paint -
Just Stop Oil (JSO) has launched high profile protests since being formed in 2022 to fight the use of fossil fuels, which scientists agree are causing global warming and climate change.
The 16 activists, including some who threw tomato soup on Vincent van Gogh's "Sunflowers" painting at London's National Gallery, are seeking to reduce or quash sentences imposed for four separate protests.
Outside court, dozens of supporters held up banners calling for it to "Protect the right to protest" and "Free political prisoners". Others sat on the ground holding photos of those in jail.
The two activists accused of throwing orange paint powder on the standing megaliths at Stonehenge entered not-guilty pleas when they appeared at Salisbury Crown Court.
They face a trial in September on two charges of damaging an ancient protected monument and intentionally or recklessly causing a public nuisance.
In the London court, five others are appealing jail terms imposed after being convicted of conspiracy to cause a public nuisance when planning to blockade a UK motorway during an online call.
Environmental NGOs Greenpeace and Friends of the Earth have joined what they call "a critically important legal appeal over the right to protest".
On Thursday, a coalition of climate and pro-Palestinian organisations plans to mobilise hundreds of people to block the road outside the appeal court in support of the activists.
Climate protests have not stopped despite the stiff jail terms.
On Tuesday, police arrested two Just Stop Oil activists for disrupting a London staging of Shakespeare's "The Tempest" starring Hollywood actor Sigourney Weaver.
The pair were charged with aggravated trespass on Tuesday and will appear in court next month, police said Wednesday.
Also on Wednesday, a group from Extinction Rebellion interrupted a London conference of insurance companies.
The activists' stunts have drawn condemnation from politicians and police and sparked a backlash among some sections of the public.
In July, five of the 16 activists who have brought the appeal were stunned after being sentenced to between four and five years in prison for planning to block the M25 motorway around London, a key transport link for the capital.
They include Roger Hallam, 58, one of the co-founders of JSO and Extinction Rebellion. His four co-accused were also jailed.
"The plain fact is that each of you some time ago has crossed the line from concerned campaigner to fanatic," judge Christopher Hehir said, during their initial sentencing.
- 'Dark day' -
The country's previous Conservative government adopted an increasingly hostile stance towards disruptive direct action, and passed a series of laws toughening punishments for such offences.
But the length of the prison terms shocked NGOs and environmental campaigners.
The UN Special Rapporteur for Environmental Defenders, Michel Forst, called it "a dark day for peaceful environmental protest and indeed anyone concerned with the exercise of their fundamental freedoms" in Britain.
CIVICUS, a global alliance of civil society organisations and activists, has said civil freedoms are being "obstructed" in the UK.
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