More aid is reaching more people inside Syria, but escalating violence across the country has left more people than ever in need. So warns Ban Ki-moon in his latest report on the Syria crisis. As the UN prepares to launch a humanitarian appeal for those affected by the conflict – the biggest single aid request in history – the secretary general’s report signals the urgent need for a step-change in international engagement with Syria. The lives of the country’s beleaguered civilians, and the future of hard-won norms of warfare, depend on it.

Every month the number of people requiring basic assistance inside Syria rises: the figure now stands at 12.2 million. More than half of those in need have been driven from their homes, and a quarter of a million people in the suburbs of Aleppo and Damascus remain besieged, trapped in the ruins of what used to be their houses.

Meanwhile, Syria’s steady descent into a human rights black hole continues. The obligations enshrined in international law hold no purchase in the country: six times as many schools were attacked over the 30 days to 16 November as the month before. Bombs and shells rain down on terrified civilians sheltering in wedding halls or awaiting treatment in hospitals. Water and power supplies are routinely cut. Murder, torture and sexual violence are part of daily life.

Since war broke out in Syria in spring 2011, our organisations have repeatedly called for a political solution to the conflict. We commend the efforts of the UN Syria envoy, Staffan de Mistura, to secure a freeze to the fighting in Aleppo. Depressingly, however, the prospects of a wider peace deal remain remote; the continuing violence can only result in greater instability in the Middle East and heightened insecurity beyond. But there are concrete steps that the warring parties, those with influence in and outside the region, and the wider international community can and should take to alleviate the Syrian people’s suffering.

First, aid must get to those who need it, regardless of whether they are in government- or opposition-held areas. Resolution 2165, the second of two security council resolutions on access in Syria, explicitly authorises UN agencies to deliver aid across borders and conflict lines. While the resolution’s adoption in July constituted a diplomatic breakthrough, it has achieved limited success on the ground: only 30 UN convoys have crossed into Syria from neighbouring states since the summer.

While we welcome Wednesday’s decision by the security council to renew the resolution for 12 months, much more needs to be done. UN agencies should ramp up their cross-border and cross-line assistance to Syria, in close cooperation with humanitarian organisations like ours, which have been delivering aid from neighbouring countries for nearly three years now. The security council, and key Middle Eastern states, should appoint senior politicians and diplomats as humanitarian envoys, mandating and empowering them to support UN initiatives aimed at improving access.

Second, states supporting the government of Syria – namely Iran and Russia – and countries with influence over opposition forces should pressure those who fail to honour their obligations under international law. It must be made clear to those who target or indiscriminately attack civilians and civilian infrastructure that such crimes cannot be committed with impunity. The recent rise in attacks on schools – once places of learning, safety and fraternity – is illustrative of the depths to which Syria’s belligerents will sink if left unchecked, and a stark reminder that an entire generation of Syrian children is being lost to this conflict.

Third, donors must fund the UN’s appeal for Syria: unless every country joins the relief effort, needs will continue to outpace resources at an ever greater rate. The provision by Lebanon, Jordan, Turkey and Iraq of shelter and protection to the more than 3 million people who have fled the country has made these four states by far the biggest humanitarian donors to date. Worryingly, they have begun to restrict access to their territory, allowing only some of the most vulnerable to get through. It is essential that these countries receive the support they need to keep their borders open, including through the resettlement of Syrian refugees outside the region.

The suffering in Syria reflects the realities of 21st-century warfare: extreme violence within states, urban battlegrounds, attacks on aid workers. But besiegement and cutting water supplies go back centuries. With its cruel mix of the modern and the medieval, and a contempt for civilian life that risks undermining international law into obsolescence, Syria is the defining humanitarian crisis of our time. Now is the moment to act.

• David Miliband is chief executive of the International Rescue Committee, Justin Forsyth is chief executive of Save the Children UK and Jan Egeland is secretary general of the Norwegian Refugee Council