Britain is on the verge of sending more support to Syrian rebels, as David Cameron warned "nothing is off the table" when it comes to the removal of President Assad.
Cameron said that the international community had already made clear that any use of chemical weapons by Syria would have "very, very severe consequences" for the Assad regime.
He described a "thoroughly dreadful" situation unfolding in Syria, with 4,000 people already dead, a hard winter coming and an "extreme" humanitarian situation on the ground.
A Syrian woman and girl carry their belongings after their home was damaged due to fighting between Free Syrian Army fighters and government forces in Aleppo
He went on: "Future generations will ask, what action did you take?
Speaking at the end of a European Council summit at which leaders agreed to look at all options for action to support a democratic future for Syria, Cameron said that military intervention was currently not on the agenda for British and EU leaders.
He said that the EU and the UK should be doing everything they can to protect civilians and to help accelerate the transition from the regime of President Bashar Assad.
Brutal fighting is unrelenting in the beleagured country, especially in the northern city of Aleppo. According to a report by Reuters on Friday, daily death tolls are exceeding 100 and sometimes 200 in recent weeks. More than 40,000 have already died in the 20-month struggle.
The crisis could worsen further still this month. The World Food Programme said as many as a million people may go hungry this winter, as worsening security conditions make it harder to reach conflict zones.
The Guardian reported that Assad forces have Deliberately targeted bakeries and food production, in an effort to cause food shortages in rebel strongholds.
David Cameron, speaking in Brussels
Cameron said in his speech on Friday: "I want a very clear message to go out to President Assad that nothing is off the table, that further support, further work, further help with the opposition - who are now better formed, better organised, better co-ordinated - is robustly on the table.
"I want us to work with that opposition, to help shape that opposition, to advise and work with that opposition, so that we can see the speediest possible transition in Syria.
"It is a very difficult situation. There are no easy answers. These things do take time. We have to understand all the complexities.
"But as a European Union and as a country - Britain - we should be doing everything we can to help speed up that transition and work towards what it says in the conclusion - and we had an important role in drafting this - that what we want is a future for Syria that is democratic and inclusive, with full support for human rights and the rights of minorities."
The summit declaration agreed by EU leaders on Syria called for a political transition "towards a future without president Assad and his illegitimate regime."
It mandated EU foreign ministers to "work on all options to support and help the opposition and to enable greater support for the protection of civilians".
Kurdish members of the FSA are seen on a tank stolen from the Syrian Army in Fafeen village
The declaration said: "The European Council is appalled by the increasingly-deteriorating situation in Syria.
"The European Council repeats its view that political transition is necessary in Syria towards a future without president Assad and his illegitimate regime.
"We support a future that is democratic and inclusive with full support for human rights and the rights of minorities. The European Council will continue to address the situation in Syria as a matter of priority."
Asked whether consideration was being given to military intervention in Syria by Britain or other EU countries, Cameron said: "No, the discussions we've been having are really about how we try and do two things.
"First of all, how do you encourage transition at the top?
Syrian children ride on the back of a pickup truck in Aleppo
"How do we work through the United Nations, how do we try and work on others in the United Nations, like the Russians, to try to move towards a position where the world comes together and pushes transition at the top and says that Assad has to go, a transition needs to take place, a move towards a democratic and inclusive Syria needs to happen?
"That's the first set of things. The second set of things is how do we help, work with, shape, support, advise, back the opposition forces who are effectively creating a transition from below?
"Now, Britain has good relations with the opposition, we've been working with them, we've now recognised the new body, we've been supplying them with non-lethal equipment and the conversation now is: 'What more should we do, what more can we do to help, advise, work with, shape and support?'
"I think what's interesting about these conclusions is that they say all options should be looked at. We've mandated the Foreign Affairs Council - the foreign ministers - to look at those issues.
"I'm not pretending there's absolute unanimity around the table, that it's time to change the sanctions regime, or anything like that. But it's on the table now that it's got to be looked at and we can't just carry on as we are."
FSA fighters pray after an attack on a Military Academy in Tal Sheer village, north of Aleppo
Cameron drew a distinction between the situation in Syria and last year's uprising in Libya, when international forces led by Britain and France provided air and sea power to prevent Muammar Gaddafi's troops from attacking civilians - effectively assisting the revolution which toppled him.
"I've always said that Syria is different to Libya," he said.
"There are extra complications and difficulties. But instead of asking what we can't do, we should be asking what can we do.
"And as you heard recently from the Americans, there are steps which, if the Syrian regime took (them) - including concerns about chemical weapons - which would have very, very severe consequences for that regime. They should understand that and understand that very clearly."