And he said Britain would continue to step up support for those trying to force Assad from power, despite warnings some rebel groups are linked to Al Qaeda.
Mr Hague acknowledged past reluctance to arm the rebels was partly because of the danger that weapons could fall into the hands of Islamist extremists.
Ministers have also been concerned at the risk of possible negative public reaction if Britain is dragged into another war in a Muslim country, ten years after the American-led invasion of Iraq.
But Mr Hague yesterday suggested the calculation about whether to arm the rebels was changing.
Jihadist: Business graduate Ibrahim al-Mazwagi has become the first British-born jihadist killed in Syria
He told Sophie Raworth on the BBC’s Andrew Marr Show: ‘These things are a balance of risk. You can reach the point eventually and the loss of life is so great that you have to do something new to save lives.’
He went on: ‘The longer this goes on, the greater the danger that extremism takes hold, the greater the danger of destabilising neighbouring countries, and the greater the extreme humanitarian distress involved. So we cannot just sit on the sidelines and watch this.
‘We will be doing more and we will have to steadily do more if there is no diplomatic or political breakthrough. The situation in Syria now is too dangerous to the peace and security of that entire region and thereby to the world to ignore it. I don’t rule anything out for the future.
‘If this is going to go on for months or years and more, tens of thousands of people are going to die and countries like Iraq and Lebanon and Jordan are going to be destabilised. It is not something we can ignore. These are the reasons why we can’t just sit it out in Syria.’
Senior Tory Edward Leigh has demanded a ‘categorical assurance that no British taxpayers’ money is finding its way to jihadists through indirect means’.
Speaking in a House of Commons debate last week, he said it was ‘essential that we do not send, or countenance sending, indirectly or directly, any arms into Syria. That would make the situation far worse.’
President Assad yesterday launched his outspoken attack on Britain.
In a rare interview he described the UK as an ‘arsonist’ which was aiding ‘terrorists’ in the country. He said Britain’s stance was ‘naive, confused and unrealistic’.
‘To be frank, Britain has played a famously unconstructive role in our region on different issues for decades, some say for centuries,’ he said.