David Cameron and Barack Obama moved the west closer to military intervention in Syria on Saturday as they agreed that last week's alleged chemical weapon attacks by the Assad regime had taken the crisis into a new phase that merited a "serious response".

In a phone call that lasted 40 minutes, the two leaders are understood to have concluded that the regime of Bashar al-Assad was almost certainly responsible for the assault that is believed to have killed as many as 1,400 people in Damascus in the middle of last week. Cameron was speaking from his holiday in Cornwall.

The prime minister and US president said time was running out for Assad to allow UN weapons inspectors into the areas where the attack took place. Government sources said the two leaders agreed that all options should be kept open, both to end the suffering of the Syrian people and to make clear that the west could not stand by as chemical weapons were used on innocent civilians.

A spokesman for No 10 said: "The prime minister and President Obama are both gravely concerned by the attack that took place in Damascus on Wednesday and the increasing signs that this was a significant chemical weapons attack carried out by the Syrian regime against its own people. The UN security council has called for immediate access for UN investigators on the ground in Damascus. The fact that President Assad has failed to co-operate with the UN suggests that the regime has something to hide.

"They reiterated that significant use of chemical weapons would merit a serious response from the international community and both have tasked officials to examine all the options. They agreed that it is vital that the world upholds the prohibition on the use of chemical weapons and deters further outrages. They agreed to keep in close contact on the issue."

The dramatic upping of the stakes came after the international medical charity Médecins sans Frontières (MSF) reported that three hospitals in Damascus had received approximately 3,600 patients displaying neurotoxic symptoms in less than three hours on the morning of Wednesday, 21 August. Of those patients, 355 are reported to have died.

Dr Bart Janssens, MSF's director of operations, said: "Medical staff working in these facilities provided detailed information to MSF doctors regarding large numbers of patients arriving with symptoms including convulsions, excess saliva, pinpoint pupils, blurred vision and respiratory distress."

He said the reported symptoms strongly indicated "mass exposure to a neurotoxic agent. This would constitute a violation of international humanitarian law, which absolutely prohibits the use of chemical and biological weapons."

France's foreign minister, Laurent Fabius, said on Saturday that "all the information at our disposal converges to indicate that there was a chemical massacre near Damascus and that the [regime of Bashar al-Assad] is responsible".

The foreign secretary, William Hague, said last week that "this is a chemical attack by the Assad regime" and "not something that a humane or civilised world can ignore".

Obama has been reluctant to commit American forces to what has become a bitter and protracted civil war. However, he said last year that use of chemical weapons would cross a "red line" triggering a more robust US response. It was confirmed yesterday that the US navy is deploying an extra missile warship to the eastern Mediterranean ahead of a summit to debate the massacre.

The summit will be held in Jordan's capital, Amman, in the first half of the week as a consensus hardens that the nerve agent sarin was used in the attack in rebel-held east Damascus early on Thursday. Biological samples taken from victims of the attack have been passed to western officials in Jordan after having been smuggled out of Syria over the past 72 hours. Questionnaires have been distributed to officials in the three most affected communities, asking for scientific and environmental details, as well as for organ tissue and clothing worn by victims.

Officials, who have not identified themselves but claim to be part of an international response, have also made phone contact with rebel officials, seeking photographs of the rockets that are thought to have carried the gas.

France, Britain and Turkey have blamed the Syrian regime for the attack, which came as its military forces were advancing into the area.

Syria has continued to deny responsibility as the UN's disarmament chief, Angela Kane, arrived in Damascus to try to negotiate access to the site of the attack for an inspection team that was sent to investigate three earlier alleged attacks. The team has been in the capital for the past six days and has been pressing for permission to make the journey – only a short distance from its hotel.

Rebel groups in the area say that they will guarantee safe passage. However, the Syrian government has not agreed and the UN fears that the journey is unsafe without a negotiated agreement.

The US secretary of state, John Kerry, spoke to Syria's foreign minister, Walid al-Moualem, on Thursday, the State Department revealed on Saturday. Kerry told him the Damascus government should have let UN inspectors have access to the site of the alleged gas attack, the department said.

Kerry called "to make clear that if, as they claimed, the Syrian regime has nothing to hide, it should have allowed immediate and unimpeded access to the site rather than continuing to attack the affected area to block access and destroy evidence," a State Department official said.

The chairman of the US joint chiefs of staff, General Martin Dempsey, will travel to Jordan along with the head of the US central command, General Lloyd Austin, and chiefs of staff from Turkey, Britain, France, Qatar, Canada, Saudi Arabia, Italy and Canada.

The addition of a US destroyer takes to four the US Mediterranean flotilla, one more than normal. US defence secretary Chuck Hagel said no decision has been made to use the warships in operations against Syria. Speaking on Friday, officials in Washington said no response to Syria would involve sending troops into the country.

Two of Syria's three main allies, Russia and Iran, have supported calls for a transparent and credible inquiry into the attack. Both accuse rebel groups of having carried out the atrocity. Syrian state television said on Saturday that its forces had found tunnels in rebel areas in which chemicals were stored.

The Lebanese militia, Hezbollah, has remained silent since Thursday. Hezbollah leaders roundly condemned car-bombings of two mosques in Lebanon's second city, Tripoli, one day later, which killed 42 and wounded hundreds. The mosques had been focal points of anti-Assad rhetoric in the largely Sunni north.

Lebanon, an unstable multi-confessional state, has been perennially on edge since the start of the Syrian uprising with occasional flare-ups in violence that threaten to drag it into the chaos consuming its powerful neighbour. The remains of 20 such rockets have been found in the affected areas, activists and local residents say. Many remain mostly intact, suggesting that they did not detonate on impact and potentially dispersed gas before hitting the ground.