Foreign Secretary William Hague will hold talks with Syrian opposition groups as the government seeks to maintain international pressure on Bashar al-Assad's regime.
Downing Street said further sanctions were being considered and warned the Assad regime that the government would not "abandon" the Syrian people.
The UN Human Rights Council will hold an emergency meeting in Geneva at the UK's request to discuss the situation in a round of diplomatic action triggered by the "sickening" massacre in Houla, where regime forces have been blamed for killing more than 100 people.
An amateur video claiming to show an injured child in Houla
An internal Syrian investigation has claimed rebels were to blame for last week's massacre in Houla, something decried as a "blatant lie" by America's ambassador to the UN .
UN Secretary-General Ban Ki-moon called on Syria to stop its attacks, saying UN observers monitoring the ceasefire brokered by envoy Kofi Annan were not there to watch the killings of innocent people.
David Cameron convened a meeting of the National Security Council yesterday as Mr Hague warned of the need for urgent action to prevent a collapse into all-out civil war.
A No 10 spokesman said: "The Prime Minister wants to be sure that we are doing all we can to bring an end to the violence in Syria and to support the process of transition.
"The National Security Council considered the range of diplomatic efforts being pursued by the Government and agreed that we need to keep working with our international partners to make clear to the Assad regime that they must comply with the Annan plan, to stop killing and maiming their own citizens and that those responsible for the brutal violence will be held accountable for their actions.
Anger: Demonstrators protest in front of the Syrian consulate in Istanbul
"They agreed that we should step up these efforts, including considering further sanctions. It is in the interest of everyone to put in place an orderly democratic transition that meets the aspirations of the Syrian people.
"The National Security Council considered all the options on the table.
"Our goal is a peaceful political transition and our focus remains on the Annan plan, but the Assad regime should not make the mistake of believing that we will abandon the Syrian people."
Mr Hague, who is in neighbouring Turkey, said: "One of the great dangers here is that Syria could collapse into a sectarian civil war in which casualties could be far greater even than the horrific scenes and the terrible toll that we have seen already.
"So there is a real urgency to this. It is hard to tell from the outside when such a collapse would take place."
Hague said he would like to see president Assad appear at the International Criminal Court (ICC) over the Houla massacre but there was little hope of the UN Security Council agreeing to refer the regime to the tribunal.
Russia and China, both permanent members of the council with the power of veto, have been reluctant to support the action demanded by the UK and others at the international institution.
Asked on Channel 4 News if the Syrian leader should be in the dock at the ICC, Mr Hague said: "Yes, that would be my personal view. Of course terrible crimes have been committed, there must be no impunity for those crimes."
"But this subject takes us back to the problem at the UN Security Council where we have united behind the Annan plan but not behind stronger action.
"To refer Syria, a country which is not a party to the International Criminal Court, to that court would require a resolution of the UN Security Council and there we, of course, are blocked."
Earlier this week Kofi Annan, the UN's envoy to Syria, warned that the country has reached a "tipping point" after the government was accused of massacring of 108 people, including 49 children.
Annan, speaking after talks with President Bashar al-Assad, called for the government to show "maximum restraint" one year since its troops began slaughtering peaceful protesters and citizens.
Warning: some of these pictures are graphic
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