The Obama administration has begun the tough task of persuading sceptical members of Congress that they should authorise military action against Syria, as secretary of state John Kerry claimed the US had evidence that sarin gas was used in an attack outside Damascus last month that killed 1,400 people.

A classified briefing was held on Capitol Hill on Sunday a few hours after Kerry made the rounds of all five Sunday talk shows in the US, mounting a strong defence of President Obama's unexpected plan to allow Congress a vote on military action against the Syrian government.

Presented with the awkward scenario that Congress would not back Obama, Kerry stressed that the president had the power to act anyway. But Kerry said he was confident of a yes vote. "We don't contemplate that the Congress is going to vote no," Kerry told CNN.

As members of Congress emerged from the briefing, it was clear that the Obama administration could not be sure of the outcome of the president's high-risk strategy. In particular, Obama could not count on his own party to deliver the votes. "I don't know if every member of Congress is there yet," said Representative Janice Hahn, a California Democrat who said she would vote no on authorising a military strike. "The room was sceptical," said Jim Himes, a Connecticut Democrat.

The briefing took place after Kerry conducted a back-to-back round of television interviews to press home the case for military strikes. Kerry, one of the leading advocates of a military assault on the regime of the Syrian president, Bashar al-Assad, outlined new evidence he said the administration had obtained about the chemical attacks outside Damascus in August. He said blood and hair samples from first responders who helped victims of the attacks had tested positive for indicators of the nerve agent sarin.

Kerry said the evidence had come through a "secure chain of custody", but not from United Nations weapons inspectors. He did not give any further details of the source for the samples, nor where or when they had been tested. The new evidence bolstered the case for action, Kerry said. "Each day that goes by this case is even stronger," he told CNN.

On Sunday, the UN secretary general, Ban Ki-moon, asked chemical weapons inspectors to speed up their investigation because of the "horrendous magnitude" of the attack in Syria.

Ban spoke by phone with the head of the team, Ake Sellström, the Swedish scientist who returned from Syria to The Hague on Saturday. The UN spokesman Martin Nesirky, briefing reporters at UN headquarters in New York, said Ban had asked for the process of analysing samples taken from the sites of the 21 August attack to be conducted as quickly as possible in keeping with the requirements of scientific stringency.

"The whole process will be done strictly adhering to the highest established standards of verification recognised by the Organisation for the Prohibition of Chemical Weapons," Nesirky said.

The samples are scheduled to be sent to laboratories in Finland and Sweden on Monday. On Friday, the UN estimated the process would take about two weeks but the findings now seem to likely to be delivered before that.

At an emergency meeting in Cairo, the Arab League called on the United Nations and the international community to take "deterrent" measures under international law to stop the Syrian regime's crimes, but could not agree on whether to back US military action. In their closing statement, Arab foreign ministers held the Assad regime responsible for the "heinous" chemical attack, saying the perpetrators should be tried before an international court "like other war criminals".

In Syria, Assad poured scorn on Obama, saying in comments carried by state media that Damascus was "capable of confronting any external aggression."

Opposition figures reacted with exasperation to what they perceive as Obama's delay in striking against Assad. While the Obama administration insists that the exclusive purpose of any such military attack would be to punish the chemical weapons attack and deter future use, the fractious and diverse opposition hopes the anticipated US strike will finally tip the military balance in their favour, something they have not managed decisively in a two-and-a-half year civil war that has killed nearly 100,000 people.

Samir Nishar of the opposition Syrian National Coalition called Obama a "weak president", according to CNN.

Kerry reacted to the Syrian opposition's evident disappointment by suggesting that Obama will not limit US involvement in the foreign civil war to cruise missile strikes tethered to chemical weapons. The administration "may even be able to provide greater support to the opposition", Kerry said. Obama authorised the provision of weapons to Syrian rebels after determining earlier this year that Assad had carried out a smaller-scale chemical attack.

Deeper involvement in the Syrian civil war has prompted reluctance within the US military to bless even a one-off military strike. General Martin Dempsey, the chairman of the joint chiefs of staff and a multi-tour veteran of Iraq, has voiced such fears for more than two years.

But Congressional hawks say Obama has not gone far enough. Senator John McCain, one of the most interventionist Republicans, said the administration needed to have a more decisive plan to topple the Assad regime. He warned against the possibility of Congress defying the president. "The consequences of a Congress of the United States over-riding a decision of the president of the United States on this magnitude are really very serious," he told Face the Nation on CBS.

McCain and his fellow Republican senator Lindsey Graham said earlier this weekend that they wanted any military campaign to "achieve the president's stated goal of Assad's removal from power, and bring an end to this conflict". Kerry, responding to McCain and Graham, said he was confident the two senators would become convinced that "there will be additional pressure" on Assad.

"A strategy is in place in order to help the opposition and change the dynamics of what is happening in Syria," Kerry told ABC News, while simultaneously denying the US would get sucked into the mire of the civil war.

Before Sunday's classified briefing, some leading legislators predicted that Obama would win a vote of the kind that his UK counterpart, Prime Minister David Cameron, unexpectedly lost last week. "At the end of the day, Congress will rise to the occasion," Representative Mike Rogers, the chairman of the House intelligence committee, told CNN. "This is a national security issue."

Others were less sure. Senator Rand Paul, a libertarian Republican, put the chances of an authorisation vote in the House of Representatives at 50-50. "I think the Senate will rubber stamp what he wants but the House will be a much closer vote," he told NBC.

Legislators estimated that between 100 and 150 members of Congress attended Sunday's classified briefing in the basement of the US Capitol, representing approximately a fifth of the Senate and House. Deputy national security adviser Antony Blinken was scheduled to be joined in the basement auditorium by four colleagues from the state department, the office of the Director of National Intelligence, the military's joint staff and the Pentagon's policy directorate.

Scott Rigell, a Virginia Republican, praised Obama for going to Congress, even as Rigell said he would not vote for the resolution. "What I wrestle with, and of course I am continuing to wrestle with this, is how do we define success and our objective, and a full understanding and consideration of the ramifications," Rigell said.

He said he was troubled by the likelihood that "the Assad regime is still there" after a strike.

Sander Levin, a Michigan Democrat, said he would support a strike, declaring himself persuaded that the Assad regime had crossed "a red line that began to be drawn a hundred years ago".

Asked how US involvement in Syria ends – with the strikes being a one-off affair or a prelude to deeper US military engagement – Levin said, "I don't think anybody's quite sure, but I think we know where we need to start."

Representative Elijah Cummings, a Maryland Democrat, said he left the briefing with questions about US strategy toward Syria, but also with questions about whether Assad would be strengthened if Congress voted against a strike, as the British parliament did last week.

Cummings said the draft authorisation for a military strike that Obama sent to Congress was "very, very broad," giving him pause. "I want to know exactly what the game plan is after this," Cummings said. "How will this strike lead, as the resolution says, to a diplomatic resolution of this issue?"

He left the briefing unsure if Obama would abide by the final vote on the Syria authorisation, which could come as early as next week, when Congress returns from summer recess. "I don't know," Cummings said. "I'm pretty sure they will, but I don't know. That's a good question."