In an impassioned speech at the UN climate action summit, the 16-year-old, who has inspired a global climate strike movement, told delegates they would never be forgiven if they failed to tackle rising temperatures.
The teenager, who travelled to the US by yacht to avoid flying, said she should not be up on stage, but should be in school on the other side of the ocean.
She said: "You come to us young people for hope - how dare you? You have stolen my dreams, my childhood with your empty words.
"How dare you continue to look away, and come here saying that you are doing enough, when the politics and solutions needed are still nowhere in sight."
She told the gathered politicians she did not believe they understood the situation, because if they did and continued to fail to act, they would be "evil" and she refused to believe that.
The teenager set out the scale of the challenge in cutting emissions to keep temperature rises to 1.5C, beyond which scientists have warned the impacts of climate change become much more severe - warning that at current rates, the remaining budget for emissions would be used up in eight-and-a-half years.
And she warned that the situation could not be solved by "business as usual" and some technological solutions.
"The eyes of all future generations are on you. If you choose to fail us, I say we will never forgive you."
She added: "Right now, right here is where we draw the line. The world is waking up, change is coming, whether you like it or not."
UN secretary-general Antonio Guterres, who convened the summit to urge increased action on tackling emissions, welcomed the young people who have been protesting over climate change.
"My generation has failed in its responsibility to protect our planet. That must change. The climate crisis is caused by us, and the solutions must come from us."
He said the world had the tools, the technology and the imperative, provided by "undeniable and irrefutable" science, and said tackling emissions would deliver other benefits in areas such as health, food security and equality.
Mr Guterres said: "There's a cost to everything but the biggest cost of all is doing nothing, the biggest cost is subsidising a dying fossil fuel industry, building more and more coal plants, and denying what is plain as day: we are in a big climate hole and to get out, we must first stop digging."
While he said the climate emergency was a race the world was losing, it is a race that could be won, and urged leaders to "lace up our running shoes and win the climate race for us all".
The UN estimates there needs to be between a three-fold and five-fold increase in efforts to cut greenhouse gases, to prevent global temperatures rising more than 1.5C above pre-industrial levels and avoid the worst impacts of climate change.
The climate action summit in New York aims to galvanise efforts by countries and businesses to close the gap between what is needed to curb global warming and current policies, which put the world on track to warm by more than 3C.
More than 60 world leaders are set to speak, including Prime Minister Boris Johnson, with heads of nations such as Finland and Germany promising to ban coal within a decade.
US President Donald Trump dropped by, listened to German Chancellor Angela Merkel's detailed pledges, including going coal-free, and then left without saying anything.
Other announcements coming forward include an alliance of some of the world's largest pension funds and investors, responsible for directing more than 2.4 trillion US dollars, who have committed to making their investment portfolios carbon neutral by 2050.
Mr Johnson is announcing that scientists will be able to use up to £1 billion of the aid budget inventing new technology to tackle the climate crisis in developing countries, alongside funding to protect wildlife.
As Mr Johnson attends the summit in New York, a group of mothers staged a pushchair protest and "climate rhyme time" action outside Downing Street and the London headquarters of Shell and BP calling for them to keep polluting fossil fuels in the ground.
Maya Mailer, from Mothers Rise Up, the group of UK mothers behind the action, said: "We are terrified mothers and we are appealing to Boris Johnson, and the bosses of Shell and BP, to start treating the climate crisis like the emergency it is: pull the plug on fossil fuels and massively ramp up investment in clean renewable energy."