A schoolgirl has stared down Donald Trump during a chance encounter in New York before she went on to give the world's most powerful leaders a sensational serve.

Climate activist Greta Thunberg, 16, crossed paths with the US President in the United Nations foyer on Monday. She was there to speak at the Climate Action Summit.

Mr Trump — who has denied climate change, called it a Chinese hoax and repealed US carbon-reduction policies — was not scheduled to attend but made the surprise visit before leaving to attend a religious freedoms meeting.

There was a lot of emotion from Greta Thunberg, of Sweden, as she addressed the Climate Action Summit in the United Nations General Assembly. Photo / AP
There was a lot of emotion from Greta Thunberg, of Sweden, as she addressed the Climate Action Summit in the United Nations General Assembly. Photo / AP

Video footage of the frosty exchange shows Mr Trump appearing to ignore Ms Thunberg as he walks straight past her with his entourage. She can be seen with her eyes fixed on him, holding her steely gaze as he moves through the corridor.

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Later, Ms Thunberg made an emotional appeal at the summit in which she chided the leaders with the repeated phrase, "How dare you".

Greta Thunberg stares down Donald Trump. Photo / Supplied
Greta Thunberg stares down Donald Trump. Photo / Supplied
Environmental activist Greta Thunberg, of Sweden, addresses the Climate Action Summit in the United Nations General Assembly. Photo / AP
Environmental activist Greta Thunberg, of Sweden, addresses the Climate Action Summit in the United Nations General Assembly. Photo / AP

Following Ms Thunberg's speech, she and 15 other children filed a complaint with the UN alleging that five of the world's major economies have violated their human rights by not taking adequate action to stop the unfolding climate crisis.

The 2019 Climate Action Summit kicked off at the UN on Monday, where world leaders gathered to discuss serious strategies to mitigate climate change. Representatives of participating nations were told by UN Secretary General Antonio Guterres to come up with "concrete, realistic plans" to further their commitments to reducing greenhouse gas emissions and get to net zero emissions by 2050.

Leader after leader told the UN that they will do more to prevent a warming world from reaching even more dangerous levels. But as they made their pledges, they conceded it was not enough.

Sixty-six countries have promised to have more ambitious climate goals and 30 swore to be carbon neutral by mid-century, said Chilean President Sebastian Pinera Echenique, who is hosting the next climate negotiations later this year. Heads of nations such as Finland and Germany promised to ban coal within a decade. Several also mentioned goals of climate neutrality — when a country is not adding more heat-trapping carbon to the air than is being removed by plants and perhaps technology — by 2050.

US President Donald Trump attend a meeting on religious freedom at United Nations headquarters before making a surprise stop at the Climate Action Summit. Photo / Getty Images
US President Donald Trump attend a meeting on religious freedom at United Nations headquarters before making a surprise stop at the Climate Action Summit. Photo / Getty Images

Mr Trump dropped by, listened to German Chancellor Angela Merkel make detailed pledges, including going coal-free, and left without saying anything.

The US did not ask to have someone speak at the summit, UN officials said. And the UN Secretary-General had told countries they couldn't be on the agenda without making bold new proposals. Even though there was no speech by Mr Trump, he was repeatedly referenced.

In a none-too-subtle gibe at Mr Trump's plans to withdraw the US from the 2015 Paris climate agreement, Chinese state councillor Wang Yi said countries "must honour our commitments and follow through on the Paris Agreement".

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"The withdrawal of certain parties will not shake the collective goal of the world community," Mr Wang said to applause.

Former New York City Mayor Michael Bloomberg, the UN's special climate envoy, thanked Mr Trump for stopping by, adding that it might prove useful "when you formulate climate policy", drawing laughter and applause on the floor of the General Assembly.

Hilda Heine, president of the Marshall Islands, said she represented "the most climate-vulnerable people on Earth".

Her tiny country has increased its emission cut proposals in a way that would limit warming to that tight goal of 1.5C since pre-industrial times. "We are now calling on others to join us," Ms Heine said.

UN Secretary-general Antonio Guterres opened the summit Monday by saying: "Earth is issuing a chilling cry: Stop." "Time is running out," Mr Guterres said. "But it is not too late."