Against a backdrop of rising ethnic and religious tension, fighting elsewhere in the Mideast and Africa, extremist attacks across the world and a warming planet, there are plenty of other issues for the 135 heads of state and government and more than 50 ministers expected to attend to try to tackle.
"It's no secret there's a lot of fear out there," US Ambassador Samantha Power told reporters on Thursday, citing the uncertainties sparked by Britain's vote to leave the European Union, the threat posed by the Islamic State extremist group, and attacks in many parts of the world by ISIS and other terrorist groups.
But Syria, where a tense ceasefire brokered by Moscow and Washington went into effect last Monday, remains at the top of the agenda at the UN General Assembly's annual ministerial meeting.
An apparently errant airstrike on Saturday in which the US military may have unintentionally struck Syrian troops while carrying out a raid against the Islamic State group could deal a crushing blow to the US-Russian-brokered ceasefire.
The ceasefire, which does not apply to attacks on ISIS, has largely held for five days despite dozens of alleged violations on both sides. The UN Security Council held a closed emergency meeting onSaturday night at Russia's request to discuss the airstrike.
The acrimonious meeting offered a harbinger of the difficulties ahead as the US and Russia remain suspicious of each other's intents in Syria. Power accused Russia of pulling "a stunt" that is "cynical and hypocritical" in calling for the meeting while not taking similar action in response to atrocities committed by Syrian President Bashar Assad's regime.
Russian Ambassador Vitaly Churkin said he had never seen "such an extraordinary display of American heavy-handedness" as displayed by Power.
The acrimony over the airstrike could spill over into a Security Council ministerial meeting on Syria scheduled for Wednesday. Russia was pushing for a resolution to endorse the cessation of hostilities and look ahead, but the US refused to make public details of the ceasefire deal citing "operational security". Churkin earlier had called the US unco-operative and said most likely "we're not going to have a resolution".
With the truce still fragile, no sign yet of humanitarian aid deliveries, and supporters and opponents of the Syrian government trading accusations, diplomats said there may be a meeting Tuesday of about 20 key countries on both sides who are part of the International Syria Support Group to chart the next steps.
The spotlight during the week is also certain to shine on three leaders, who are all scheduled to speak at the assembly's opening ministerial session on Tuesday morning.
UN Secretary General Ban Ki-moon who steps down on December 31, and US President Barack Obama who will leave office in January, will be addressing the 193-member world body for the last time. And British Prime Minister Theresa May will be making her debut on the world stage less than three months after the vote to leave the European Union.
In UN corridors and at private meetings, the question of Ban's successor will be a hot topic. Portugal's former Prime Minister Antonio Guterres has topped all four informal polls in the Security Council but he could be vetoed, possibly by Russia, and there are constant rumours of new candidates throwing their hats in the ring.
The US presidential race is already a hot topic at the UN, and no doubt leaders will be privately discussing the impact of a victory by Hillary Clinton, and especially Donald Trump, on the United Nations where the United States is the largest financial contributor and has veto-wielding power in the Security Council.
In one of the week's highlights, the secretary general has invited leaders to a first-ever UN Summit on Refugees and Migrants on Monday.
According to the Office of the UN High Commissioner for Refugees, an "unprecedented" 65.3 million people were displaced at the end of 2015, an increase of more than 5 million from a year earlier and the highest number since WW II. They include 21.3 million refugees, 3.2 million asylum seekers, and 40.8 million people internally displaced within their own countries.
"''More countries must resettle more people who have been forced from their homes," Ban told reporters on Wednesday. "And everyone, everywhere, must stand up against the animosity that so many refugees, migrants and minority communities face."
The political declaration set to be adopted calls for separate Global Compacts for refugees and migrants to be adopted within two years. But human rights groups complained that it was watered down, eliminating Ban's proposal to resettle 10% of the world's refugees annually.
At a follow-up summit on Tuesday called by Obama, at least 45 countries are expected to make pledges that will meet or exceed US goals of increasing humanitarian aid by $3bn, doubling resettlement and lawful admission spots, and increasing access to education for one million
youngsters and access to employment by one million, a US official said, speaking on condition of anonymity ahead of the summit.
"We are not going to solve the refugee crisis on Tuesday," US envoy Power said, "but I think you'll see an important show of political will from leaders around the world".
According to the United Nations, 545 meetings have been requested and Ban will take part in 62 events. The UN chief, who has made climate change a top priority, has organised an event on Wednesday for countries to deliver their ratifications of the Paris Declaration to tackle global warming.
He is hoping to get the required 55 countries representing 55% of greenhouse gas emissions, if not on Wednesday, then by the end of the year. Nigeria's Foreign Minister Geoffrey Onyeama, whose government is battling the insurgency by Boko Haram Islamic extremists, told reporters on Friday that addressing "this global phenomenon of terrorism" will be high on his country's agenda along with tackling the UN development goals for 2030 and promoting a new UN body to focus on youth.
The Security Council is holding a ministerial meeting on Thursday on improving aviation security, and it could meet again if agreement is reached on a resolution to support the nuclear test ban treaty which will likely single out North Korea, the only country to conduct tests in the 21st century.
The parties to the Iran nuclear deal are also scheduled to meet on Thursday as well as the Quartet of Mideast mediators - the US, UN, EU and Russia - who are trying to get Israel and the Palestinians back to the negotiating table.