More than 140 heads of state and government fly in to New York this week for the United Nations general assembly amid apprehension that international order is unraveling at an accelerating pace, while the world's leaders seem ever less willing or able to deal with the proliferating threats.

The UN's humanitarian agencies are in danger of being completely overwhelmed by the multiple crises. Ebola is spreading rapidly across West Africa, swamping rickety national health systems and a thus-far underfunded UN effort to stop its advance. The spread of Islamic State (Isis) extremists in the Middle East, feeding on the destruction of the Syrian civil war and exposing the weakness of the Iraqi state, has similarly outpaced patchy international efforts at containment.

New conflicts have flared while the old ones have burned on in the absence of concerted effort to quench the flames. Much of Gaza lies in ruins and there is no longer even a pretence at regenerating Israel-Palestinian peace talks. Meanwhile, war has returned to the edges of Europe, with the dismemberment of Ukraine. The conflicts in South Sudan and the Central African Republic, which seemed among the world's most pressing concerns at the start of the year, continue to inflict enormous human cost yet are likely to draw scant attention at the world's talking shop this week, distracted by so many fresh disasters.

Ban summed up the mood of foreboding hanging over the UN headquarters in midtown Manhattan, saying the world was "living in an era of unprecedented level of crises." The degree of deadlock among the traditional world powers is probably not unprecedented given the poor record of statesmanship displayed over the decades at the United Nations, but the zero-sum atmosphere in relations between Russia and the West is at a nadir not witnessed since the Cold War. Russia's annexation of Crimea represented a direct challenge by a permanent member of the security council to core UN principles underpinning international security. And the bitterness surrounding Ukraine, compounding already deep divisions over Syria, has seeped into security council discussions on a host of other issues.

"The UN is grappling with crises on every level and Ukraine is poisoning the organisation from the head down," said Richard Gowan, at the Center on International Cooperation at New York University. "It does feel like a particularly dreadful year."

The one exception to the confrontational climate at the security council this year has been its deliberations on fighting the Ebola virus. Before the leaders even arrived, the council made history at ambassadorial level on Thursday, passing a resolution declaring Ebola a threat to international peace and security, calling on countries to send medical workers and supplies to combat it. The UN established an emergency mission to contain the spread of the disease in Liberia, Sierra Leone and Guinea. Ban will chair a further summit meeting on implementing the resolution this week. "Ebola represents an opportunity for the UN in a way," Gowan said. "It is one of those crises in which there are no conflicting interests. There is no pro-Ebola faction. And dealing with it involves using all parts of the UN system. It's a classic international problem requiring a common response."

Ban is seeking a similarly common response to another longstanding and growing international challenge – climate change, but with significantly less success. The general debate is starting a day later than usual this year, on Wednesday, so that the world's leaders can attend a global summit on the issue on Tuesday. But the leaders of the world's three biggest countries, Russia India and China, will not be attending, claiming other commitments. The actor Leonardo di Caprio, named the latest UN "messenger for peace" on climate change, will address the Tuesday summit, but his star power is unlikely to make up the gaping hole in international commitment on the issue.

On Syria, the task of building a political and military coalition against the extremist group has been done outside the framework of the UN. A security council meeting will not address the role in the conflict of the Assad regime in Damascus, which – despite Isis's brutality – is still responsible for far more civilian deaths, according to Human Rights Watch.

On Wednesday afternoon, Barack Obama will chair a security council summit session on Syria, but it will address only the Isis threat and common ways of stopping the flow of foreign fighters to the conflict, on which there is at least agreement in the council on principle. But the task of building a political and military coalition against the extremist group has been done outside the framework of the UN. The council meeting will not address the role in the conflict of the Assad regime in Damascus, which – despite Isis's brutality – is still responsible for far more civilian deaths, according to Human Rights Watch. Despite the regime's continuing use of barrel bombs and air strikes against residential areas, Russia remains a staunch ally of Assad inside the council, blocking any punitive measures.

The one chink of light on the international scene atfrom last year's general assembly also seems less bright 12 months on. The last minute mobile phone conversation in 2013 between President Barack Obama and his Iranian counterpart, Hassan Rouhani, as the latter drove to the airport, boosted hopes of a historic thaw in relations between the two countries. It helped create conditions for a breakthrough interim deal in November on Iran's nuclear programme, freezing it in place and partly reversing some elements in return for a slight relaxation in western sanctions. However, progress towards a more comprehensive agreement has been faltering. International talks due to conclude in July have been given a six-month extension, but optimism around the negotiations is fading.

"Even optimists recognise that the prospects are dimming for a comprehensive nuclear deal between Iran and the West," Trita Parsi, the head of the National Iranian American Council, warned in a commentary for Foreign Policy magazine.

"Rouhani's conservative opponents fear that a nuclear deal will pave the way for a major shift in Iran's foreign-policy orientation and further push the conservatives away from Iran's centres of power," Parsi argued. He added: "Simply put, Iran can afford to say no to a deal that doesn't meet its bottom line requirements."