UN Secretary-General Antonio Guterres, while saluting efforts for global cooperation, warned of a dire state of the planet.
"A winter of global discontent is on the horizon," Guterres said as he opened the annual General Assembly.
"Trust is crumbling, inequalities are exploding, our planet is burning. People are hurting -- with the most vulnerable suffering the most."
With global temperatures rising and a chunk of Pakistan the size of the United Kingdom recently under water, Guterres lashed out at fossil fuel companies and the "suicidal war against nature."
"Let's tell it like it is -- Our world is addicted to fossil fuels. It's time for an intervention. We need to hold fossil fuel companies and their enablers to account," Guterres said.
He called on all developed economies to tax profits from fossil fuels and dedicate the funds both to compensate for damage from climate change and to help people struggling with high prices.
"Polluters must pay," Guterres said.
- Ukraine in focus -
The summit was disrupted after the death of Queen Elizabeth II, with President Joe Biden of the United States, by tradition the second speaker on the opening day, instead due to speak on Wednesday.
Day one features French President Emmanuel Macron and German Chancellor Olaf Scholz, the leaders of the two largest economies of the European Union, which has mobilized to impose tough sanctions over Russia's invasion of Ukraine.
"This year, Ukraine will be very high on the agenda. It will be unavoidable," top EU diplomat Josep Borrell told reporters in New York.
"There are many other problems, we know. But the war in Ukraine has been sending shock waves around the world."
German Foreign Minister Annalena Baerbock vowed to support countries hardest hit by the fallout from the war as she headed to the General Assembly on Tuesday.
"The brutality of Russia's war of aggression and its threat to the peace order in Europe have not blinded us to the fact that its dramatic effects are also clearly being felt in many other regions of the world," Baerbock said.
Russian Foreign Minister Sergei Lavrov was visiting despite a hostile reaction from the United States.
With the Ukraine war leading to a global grain crisis, hunger is another major issue on the agenda. More than 200 NGOs called for urgent action from leaders gathered for the General Assembly to "end the spiraling global hunger crisis."
"Around the world, 50 million people are on the brink of starvation in 45 countries," they said, adding that as many as 19,700 people are estimated to be dying of hunger every day, which translates to one person every four seconds.
- Talks between rivals -
Other leaders to speak Tuesday include Turkish President Recep Tayyip Erdogan, who has staked out ground as a broker between Russia and Ukraine, including through a deal to ship out badly needed grain to the world.
Erdogan is also expected to meet in New York with Israeli Prime Minister Yair Lapid, a dramatic rebound in relations after the Turkish leader's strident criticism of the Jewish state's treatment of Palestinians.
In the type of last-minute diplomacy common at previous UN sessions, US Secretary of State Antony Blinken convened a first meeting of the foreign ministers of Azerbaijan and Armenia since a flare-up in fighting.
Also high on the agenda for the UN week will be Iran, whose hardline president, Ebrahim Raisi, is traveling to the General Assembly for the first time and met Tuesday with France's Macron.
In a US television interview ahead of his arrival, Raisi said Iran wanted "guarantees" before returning to a nuclear deal that former president Donald Trump trashed in 2018.
Biden supports a return to the 2015 agreement, under which Iran drastically scaled back nuclear work in return for promises of sanctions relief.