Cameron, however, said he was convinced the regime of President Bashar al-Assad was behind the attack that killed hundreds in a Damascus suburb last week.
British parliamentarians are to vote on a motion backing military action against Syria in principle, but noting that "every effort" must be made to secure UN Security Council backing. A second vote would be needed to authorize British involvement.
Cameron indicated that a military response to the use of chemical weapons in Syria is not intended to topple Assad’s regime.
"The question before the House today is how to respond to one of the most abhorrent uses of chemical weapons in a century, slaughtering innocent men, women, and children in Syria," he said. "It is not about taking sides in the Syrian conflict, it is not about invading, it is not regime change or even working more closely with the [Syrian] opposition. It is about the large scale use of chemical weapons and our response to a war crime, nothing else."
Cameron, however, said it was "unthinkable" that Britain would launch military action against Syria if there was strong opposition at the UN Security Council. Security Council members Russia and China oppose military intervention in Syria.
Earlier, U.S. President Barack Obama said the United States has "concluded" that the Syrian government carried out the attack, which killed hundreds, but has not made a decision yet on military action.
Speaking on U.S. public television on August 28, Obama said he is still evaluating possible military options to punish Syria for the August 21 attack in the suburbs of Damascus that activists say killed hundreds of people.
"If, in fact, we make a choice to have repercussions for the use of chemical weapons, then the Assad regime, which is involved in a civil war trying to protect itself, will have received a pretty strong signal that, in fact, it better not do it again," Obama said.
Obama suggested any possible U.S. military response would be limited in scope.
"I have no interest in any kind of open-ended conflict in Syria, but we do have to make sure that when countries break international norms on weapons, like chemical weapons that could threaten us, that they are held accountable," he said.
WATCH: Protesters rally in London against a possible strike against Syria
Meanwhile, UN Secretary-General Ban Ki-moon told reporters that UN inspectors investigating an alleged chemical weapons attack in Syria will report back to him immediately after they leave the country.
"[The UN chemical weapons inspectors] will continue investigation activities until tomorrow, [August 30], he said, and they will come out of Syria by [the next] morning, and will report to me as soon as they come out of Syria."
Ban said on August 29 that the inspectors' conclusions will be shared with members of the UN Security Council, but he did not specify when that might be.
Russian President Vladimir Putin and German Chancellor Angela Merkel noted in a telephone conversation on August 29 that it is important for the UN Security Council to consider a report of the chemical weapon inspectors about possible facts concerning the use of chemical weapons in Syria.
Russia says any military action would be a "challenge" to the UN Charter.
At the UN Security Council on August 28, Russia blocked a draft resolution proposed by Britain that would have authorized the use of force in response.
On August 29, Washington accused Russia of intransigence.
"We are invested in the UN process,” U.S. White House deputy spokesman Josh Earnest told reporters. " At the same time we are currently seeing that process circumvented by an intransigent Russia that is refusing to allow the UN to hold Syria accountable. So what the [U.S.] President [Barack Obama] will do is he will make a decision about an appropriate response based on the national security interests of the United States of America."
On August 29, Iran's Supreme Leader Ayatollah Ali Khamenei again warned against any attack on Syria, a close ally.
"Any kind of intervention by a foreign power, be it in Syria or another country, will only serve those who seek war and conflict and will only increase hatred of those countries who meddle," he said.
On the same day, China cautioned against prejudging the results of the UN inspections.
Syrian President Bashar al-Assad said on August 29 that Syria will "defend itself against any aggression."