After a year spent protesting on the streets, it was Greta Thunberg's moment on the world stage, and she did not disappoint, accusing leaders of betrayal and repeatedly demanding "How dare you?" in a raw, emotional speech.

Since landing on U.S. shores on a sailboat in August, the Swedish teen has spoken only briefly at public events, preferring to pass the mic to lesser-known activists so that more voices are heard.

Not so at Monday's Climate Action Summit, convened by UN chief Antonio Guterres to reinvigorate the Paris agreement, where Thunberg was determined to make the most of the allotted time.

She began by telling the audience: "My message is that we'll be watching you," eliciting some laughter.

But it soon became clear that humor was not what she was going for.

"This is all wrong," Thunberg said, becoming visibly angry. "I shouldn't be up here. I should be back at school on the other side of the ocean."

"Yet, you come to us young people for hope. How dare you?" the 16-year-old, who has taken time off from her education to focus on activism, thundered.

"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.

"We are in the beginning of a mass extinction, and all you can talk about is the money and fairy tales of eternal economic growth. How dare you!"

'You are failing us'

She said that in her talks with leaders, she had been told that the youth were being heard and the urgency was understood.

"But no matter how sad and angry I am, I do not want to believe that, because if you really understood the situation and still kept on failing to act, then you would be evil, and that I refuse to believe."

Shifting gears for a moment from powerful rhetoric to wonkishness, she reeled off a litany of damning facts and statistics to build up her argument.

She said the popular goal of reducing emissions by 50 percent by 2030 only gave the planet a 50 percent chance of avoiding a long-term temperature rise of 1.5 degrees Celsius, vital to avert catastrophe, and that "a 50 percent risk is simply not acceptable to us."

"There will not be any solutions or plans presented in line with these figures here today because these numbers are too uncomfortable, and you are still not mature enough to tell it like it is."

"You are failing us," she concluded. "But the young people are starting to understand your betrayal.

"The eyes of all future generations are upon you, and if you choose to fail us, I say, we will never forgive you!"

The speech lit up Twitter and the truth of Thunberg's words was borne out by the lack of major commitments that followed by the world's biggest emitters, despite much pre-summit hype.