Last week, the prime minister suffered a humiliating defeat in the House of Commons over a motion which would have seen the UK back military intervention against the regime of the Syrian president.
Violent clashes between Bashar Assad's troops and rebel forces have escalated, amid reports that the Syrian government has used deadly chemical weapons in the conflict.
"The world needs to take a very tough response to things like chemical weapons attacks," Mr Cameron said.
"I accept that Britain can't be part - and won't be part - of any military action on that front, but we must not in any degree give up our utter revulsion at the chemical weapons attacks that we have seen and we must press this point in every forum that we are a member."
If no action is taken following President Obama's red line and if no action is taken following this appalling use of chemical weapons, you have to ask yourself what sort of Armageddon are the Syrian people going to be facing?
Prime Minister David Cameron
Speaking about the Syrian opposition, the prime minister added: "They are standing up for millions of Syrians who have been bombed and blasted out of their houses.
"Those are the people you need to talk to in the refugee camps in Jordan and elsewhere - to see how they feel about how badly the rest of the world is currently letting them down."
Labour politicians - plus 30 of Mr Cameron's own Conservative Party, nine Liberal Democrats and 10 Northern Ireland MPs - voted against the prime minister's motion.
But the party's leader Ed Miliband said: "Last week's vote was not about Britain shirking its global responsibilities. It was about preventing a rush to war."
The issue of Syria is now set to dominate the agenda of the G20 summit, which opens in St Petersburg on Thursday.
Russian President Vladimir Putin remains unconvinced about the validity of the reports regarding the use of chemical weapons by the Assad regime.
But he has also said that Russia has not ruled out supporting a UN resolution on military strikes, if compelling evidence of such chemical attacks was presented.
Stating that it would be "absolutely absurd" for the Syrian government to use such weapons at a time when it was holding sway over the rebels, Mr Putin said evidence must be passed to the UN.
"And it ought to be convincing," he added.
"It shouldn't be based on some rumours and information obtained by special services through some kind of eavesdropping, some conversations and things like that."
Just a day ahead of the G20 summit, US President Barack Obama warned that "the world set the red line" when it was agreed that the use of chemical weapons was abhorrent and forbidden.
My credibility is not on the line; the international community's credibility is on the line.
US President Barack Obama
The president believes that intelligence proves the Assad regime has now overstepped that red line and insists that failing to act would send a signal that "somebody who is not shamed by resolutions can continue to act with impunity".
As an opponent of the war in Iraq, Mr Obama added that he was "not interested in repeating mistakes of is basing decision on faulty intelligence" - in a reference to information regarding the presence of weapons of mass destruction.
But he said that "the accumulation of evidence gives us high confidence that Assad carried this out".
Mr Obama asked: "After we've gone through all this, are we going to try to find a reason not to act?
"If that is the case, then I think the world community should admit it because you can always find a reason not to act."
On Wednesday, rows of white gravestones were laid out in Buoy Square in Belfast city centre to represent just some of the 100,000 people killed in the conflict in Syria.
Oxfam Ireland volunteers also laid white roses by the graves as part of calls to find a peaceful solution to what the charity calls "the worst humanitarian crisis the world has seen in a generation".