William Hague has said there is an increasing risk of civil war in Syria and the government must implement an international plan to stop violence.
Speaking in Moscow, the UK foreign secretary said Friday's massacre in the town of Houla was "deeply disturbing" and had "drawn the attention of the world" to events in the country.
UN envoy Kofi Annan is due to hold talks with President Assad on Tuesday.
Mr Hague said the Annan plan was the "only hope" for stability in Syria.
He was speaking after holding talks with his Russian counterpart Sergey Lavrov, talks which were dominated by the violence of Syria.
The United Nations has condemned Syria for its use of heavy weaponry after at least 108 people were killed, including many children, in the Syrian town.
'Cycle of violence'
The UK has said it was "absolutely sickened" by the killings and the Syrian charge d'affaires will be summoned to the Foreign Office later to hear the government's criticism.
"I think we are all deeply disturbed by what we have seen over the weekend that has illuminated the continuing killing and abuse in Syria," he said.
Mr Hague said the Assad government must implement a six-point put forward by Mr Annan, a former UN secretary general, which would see an immediate end to violence and for a path towards a "more pluralist and democratic" system of government in the country.
"The Annan plan is the best hope for Syria, at the moment the only hope for Syria, to try and break the cycle of violence.
"It is not as if the alternatives in Syria are the Annan plan or the Assad regime retaking control of the country. The alternatives are the Annan plan or ever-increasing chaos in Syria and a descent closer and closer to all-out civil war and collapse.
"There needs to be a fundamental change in the approach of the Assad regime if Syria is to be saved from ever greater chaos and disorder."
Russia and China have blocked previous attempts to impose UN sanctions on Syria. Russia views Syria as an ally in the region.
Mr Lavrov said Russia wanted to see an end to violence by all sides in Syria and a political process based on respect for Syria's "sovereignty, territorial integrity and independence".
"We are dealing with a situation in which both sides evidently had a hand in the deaths of innocent people," he said.
The UN said 49 children and 34 women were among Friday's dead. The Syrian authorities have claimed anti-government forces were responsible for the deaths.
The unrest in Syria has killed at least 10,000 people since protests against President Assad broke out in March 2011.
For Labour, shadow foreign secretary Douglas Alexander said urgent progress was needed during Mr Annan's visit to Damascus.
"Condemnation from the UN Security Council of the appalling crimes perpetrated by the Syrian regime is welcome but insufficient given the slaughter," he said.
"It was right for William Hague to travel to Moscow to make clear the responsibility of the international community, including Russia, to come together in a stronger and more effective diplomatic response."
Meanwhile, Syrian Olympic Committee chairman Mowaffak Joma has said the UK "has no right" to deny their athletes access to the London 2012 Olympic games.
Deputy Prime Minister Nick Clegg had said Syrian delegation members with connections to the regime will not be allowed entry.
Mr Joma said the Olympic charter forbids host countries from banning athletes.