Video report by ITV News Washington Correspondent Robert Moore
The 16-year-old told delegates they would never be forgiven by future generations if they failed to tackle rising temperatures.
“This is all wrong. I shouldn’t be up here. I should be back in school on the other side of the ocean,” she said.
“You have stolen my dreams and my childhood with your empty words, yet I’m one of the lucky ones.
“People are suffering. People are dying, entire ecosystems are collapsing.
“Yet, you all come to us young people for hope. How dare you?"
As Ms Thunberg continued delivering her scathing words, tears welled in her eyes.
“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 said.
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 warned that at current rates, the remaining budget for world emissions would be used up in eight-and-a-half years, if they were to simple aim to keep world temperatures rising 1.5 degrees above pre-industrial era levels.
Ms Thunberg 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.”
This comes as the young activist inspired millions of people across the globe - young and old - to take to the streets in the biggest environmental protest in history last Friday.
UN secretary-general Antonio Guterres, who convened the summit to urge increased action on tackling emissions, welcomed the protest.
Mr Guterres said the climate emergency was a race the world was losing, but 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”.
He said: “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.
“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," he said.
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 1.5 degrees 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.
Based on current policies , the world is on track to warm by more than 3 degrees.
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.
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.
US President Donald Trump dropped by and listened to German Chancellor Angela Merkel’s detailed pledges, including going coal-free, however left without saying a word.
Eagle-eyed vewers of the summit spotted Ms Thunberg seemingly glaring at President Trump as he walked past her.
She has previously stated she would not meet Mr Trump on her US trip.
Prime Minister Boris 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.”