Opening the UN General Assembly debate in New York, Secretary-General Ban Ki-moon has warned that human rights are "under attack" throughout the world.
Addressing the 193-nation assembly on September 24, Ban painted a grim picture of the world, saying, "This year, the horizon of hope is darkened."
"It may seem as if the world is falling apart, as crises pile up and disease spreads," he added.
Ban drew up a list of world crises, citing the "new depths of barbarity" carried out by Islamist militants in Iraq and Syria, fighting in Ukraine, and the Gaza war, among others.
"From barrel bombs to beheadings, from the deliberate starvation of civilians to the assault on hospitals, UN shelters, and aid convoys, human rights and the rule of law are under attack," he said.
The UN chief called for international assistance to solve the crises, saying that leadership is about "finding the seeds of hope and nurturing them into something bigger."
"That is our duty," he said. "That is my call to you today."
More than 140 presidents, prime ministers, monarchs, and ministers will take part in the annual gathering, which runs to September 30.
The threat posed by Islamic State militants is expected to top the issues raised by leaders, along with the spread of the Ebola virus in western Africa, plus Russia's actions in Ukraine.
In her speech to the General Assembly, Brazilian President Dilma Rousseff said developing countries should be better represented in international financial institutions -- such as the International Monetary Fund and the World Bank -- that otherwise are in danger of losing legitimacy.
"The delay in the expansion of voting rights of developing countries in these institutions is unacceptable," she said.
The opening of the UN meeting come after a UN climate-change summit agreed to widen the use of renewable energy and raise billions of dollars in aid for developing countries.
The one-day UN summit on September 23 set goals to halt losses of tropical forests by 2030, improve food production, and hike the share of electric vehicles in cities to 30 percent of new vehicle sales by 2030.
The targets are meant to help prepare a 200-country summit in Paris in late 2015 to finalize a deal to slow rising greenhouse-gas emissions.
With reporting by AFP, AP, and dpa