The United Nations Security Council authorised countries yesterday to "take all necessary measures" to fight the jihadist group, in a resolution a week after the Paris attacks that claimed 130 lives.
Cameron called the vote on the French-drafted text an "important moment".
"The world has united against ISIL (Islamic State). The international community has come together and has resolved to defeat this evil, which threatens people of every country and every religion," he said in a statement.
Britain is taking part in airstrikes on Islamic State targets in Iraq and the government intends to seek parliamentary approval to extend these to Syria -- if it can secure a consensus across parties.
However, Jeremy Corbyn, the pacifist leader of the main opposition Labour Party, is against any such action.
In 2013, Cameron's government suffered a scarring defeat in parliament over its plan to join international military action over the use of chemical weapons by Syrian President Bashar al-Assad.
"I will continue to make the case for us to do more and to build support in parliament for the action that I believe is necessary for Britain to take to protect our own security, as part of a determined international strategy.
The UK Independence Party (UKIP), which leads the
"Brexit" pack, dismissed the Prime Minister's claims.
Party leader Nigel Farage told the BBC: "All he has asked for is some minor changes to migrant benefits and a couple of promises that might go in the next treaty. The truth of it is he can't deliver this deal because the European Parliament can strike down the benefits deal and the European Court of Justice can rule out everything else.
Renegotiations of the UK's relationship with Europe were finalised on Friday night after marathon talks at a two-day summit in Brussels.
The agreement, which will take effect immediately if the UK votes to remain in the EU, includes changes to allow curbs on migrant welfare payments, safeguards for Britain's financial services and making it easier to block unwanted EU regulations.
The UK's Election Commission takes charge of the referendum planning as soon as the date is officially cleared by Parliament, where it is expected to sail through with a majority.
The vote was in favour of staying in, but there have been growing calls from the public and politicians for another vote.
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