Teenage climate change activist Greta Thunberg has opened the United Nations Climate Action Summit with an angry condemnation of world leaders for failing to take strong measures to combat climate change.

"How dare you," she said.

Days after millions of young people took to the streets worldwide to demand emergency action on climate change, leaders gathered for the annual UN General Assembly were to try to inject fresh momentum into stalling efforts to curb carbon emissions.

The teenager, visibly emotional, said in shaky but stern remarks that the generations that have polluted the most have burdened her and her generation with the extreme impacts of climate change.

"This is all wrong. I shouldn't be up here. I should be back in school on the other side of the ocean yet you all come to us young people for hope. How dare you," she said.

"You have stolen my dreams and my childhood with your empty words," she said.

UN Secretary-General Antonio Guterres, who convened the summit, had warned governments ahead of the event that they would have to offer action plans to qualify to speak at the summit, which is aimed at boosting the 2015 Paris Agreement to combat global warming.

In his opening remarks, he tried to capture the urgency of climate change and called out the fossil fuel industry.

"Nature is angry. And we fool ourselves if we think we can fool nature, because nature always strikes back, and around the world nature is striking back with fury," Mr Guterres said.

"There is a cost to everything. But the biggest cost 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: that we are in a deep climate hole, and to get out we must first stop digging," he said.

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World leaders including Taoiseach Leo Varadkar, German Chancellor Angela Merkel, French President Emmanuel Macron and Indian Prime Minister Narendra Modi addressed the one-day gathering, alongside companies working to promote renewable energy.

US President Donald Trump and Brazilian President Jair Bolsonaro, both climate change sceptics, had not been expected to attend, but Mr Trump made a brief unscheduled appearance this afternoon.

With climate impacts such as extreme weather, thawing permafrost and sea-level rise unfolding much faster than expected, scientists say the urgency of the crisis has intensified since the Paris Climate Accord was agreed.

The agreement will enter a crucial implementation phase next year after another round of negotiations in Chile in December.

Pledges made so far under the agreement are nowhere near enough to avert catastrophic warming, scientists say, and last year carbon emissions hit a record high.