Syria has met the first deadline set by arms inspectors for the destruction of its chemical weapons after their use in Damascus in August – amid warnings that the international community is failing to get to grips with the wider crisis.

The Organisation for the Prevention of Chemical Weapons (OPCW) announced on Thursday that Syria's declared chemical weapons production and mixing facilities had all been destroyed – a day ahead of the target it had set.

It means that Syria can no longer produce any new chemical weapons, although it has yet to start destroying its existing stockpile. This is estimated at about 1,000 tonnes of chemicals and weapons, including mustard gas and the deadly nerve agent sarin.

Hundreds of people were killed near Damascus on 21 August in the deadliest chemical weapons incident since Saddam Hussein's forces used poison gas in the Kurdish town of Halabja in 1988. The US, Britain and France – and the Syrian opposition – all blamed the Syrian government, which denies responsibility and pointed the finger at the opposition.

Rebels fighting to overthrow President Bashar al-Assad say September's US-Russian deal on chemical weapons – which averted the threat of US air strikes – has bolstered the government. Assad has said he will attend peace talks in Geneva but insists first on an end to all foreign support for the opposition, which is deeply divided over taking part.

David Reeths of IHS Jane's Consulting, hailed the OPCW's achievement in a conflict zone where 100,000 people have been killed in two and a half years. But he warned that there was a "significant level of uncertainty" surrounding the true status of the Syrian chemical weapons programme because inspectors had been unable to visit two of declared weapons sites due to unacceptable levels of risk.

"Crucially, the OPCW is only certifying functional destruction of Syrian self-declared equipment from self-declared sites," Reeths said. "Because little time has passed between the declaration and this certification, there is much greater uncertainty than usual surrounding the declaration itself."

The deteriorating humanitarian situation in Syria provoked a warning on Thursday from David Miliband, a former British foreign secretary and head of the International Rescue Committee. Miliband backed the calls of the United Nations and international charities for a ceasefire after confirmation of a polio outbreak among Syrian children, calling it a "terrifying indication of what can happen when a country falls apart under the weight of war".

Speaking on BBC Radio 4's Today programme, Miliband said doctors and aid workers were being targeted as a "disaster of epic proportions" gripped the country. The outbreak was a "shocking, jolting" reminder to the international community that while there may be progress on chemical weapons, there was still misery, death and decay in Syria and its neighbouring countries, where there are seven or eight million displaced people.

Claire Spencer, of the Chatham House thinktank in London, commented: "Addressing the chemical weapons issue is only part of the challenge, and until and unless the collective security of the Syrian people is put at the centre of collective diplomatic energies, no piecemeal solution will address or resolve the underlying conditions for the restoration of peace. Even if highly significant, the chemical disarmament process has assumed a disproportionate role in international diplomacy, at the short- to medium-term cost of resolving the core conflict."

Britain's Foreign Office said in a statement: "While the challenging work of the OPCW has reached an important first milestone, it brings no relief to the Syrian people. The Assad regime continues to use artillery, air power and siege tactics against civilians, with thousands killed every month. As winter approaches, the humanitarian situation grows more acute with millions left vulnerable.

"The regime has shown it can facilitate access for OPCW inspectors – it needs to show the same commitment to ensuring humanitarian aid reaches those in need. Only a political solution will end the suffering; we must begin the Geneva II process as soon as possible."