The US is working with Britain to strengthen elements of the Syrian opposition, Barack Obama has told a White House press conference with David Cameron, where the two leaders sought to project a united front in seeking a political solution on Syria.

The British prime minister said in a US radio interview that Britain had not ruled out taking tougher action against Bashar al-Assad's regime, but later told reporters that his government has not made a decision to arm the Syrian opposition.

He announced, however, that Britain would double its non-lethal aid to the opposition over the next year and that it was looking at ways to provide more technical assistance to the rebels.

"The challenges remain formidable, but we have an urgent window of opportunity before the worst fears are realised," Cameron said at the White House on the first day of a visit to the US, where he had been expected to tell the US president that he believes Russia's Vladimir Putin may be prepared to adopt a more flexible approach on Syria.

However, Obama also used the conference to inject a note of caution after Washington and Moscow had raised hopes last week with an agreement to try to arrange an international peace conference on Syria.

While vowing to work to bring the Syrian government and rebels to the negotiating table in coming weeks, Obama warned that a "combustible mix" of regional meddling and Islamist militancy would make it hard to halt the country's civil war.

"I'm not promising that it's going to be successful," he said of the diplomatic effort, adding that once "the furies have been unleashed … it's very hard to put things back together."

"There are going to be enormous challenges … even if Russia is involved, because we still have other countries like Iran, and we have non-state actors like Hezbollah that have been actively involved."

Cameron and Obama agreed on the need to keep up pressure on Assad to step aside and make way for a political transition.

Cameron announced that the UK would be providing £30m in new aid to Syria, strictly for humanitarian relief, and an additional £10m in "non-lethal support" to strengthen the Syrian opposition.

"Syria's history is being written in the blood of her people and it is happening on our watch," said Cameron, who added that the UK would increase efforts to "support and to shape the moderate opposition".

The new humanitarian support of £30m takes the UK's total contribution to the Syria humanitarian crisis to £170m, according to Downing Street.

• This article was amended on 14 May 2013. The additional support is for people in need inside Syria, not refugees as the original said.