Cameron said he would make a statement in the House of Commons on Thursday as he steps up pressure for MPs to vote in favour of joining international action against Islamic State jihadists following the November 13 attacks in Paris, which killed 130 people.
His comments came as he presented the Strategic Defence and Security Review (SDSR), which maps Britain's military strategy for the next five years.
"As the murders on the streets of Paris reminded us so starkly, ISIL (another term for IS) is not some remote problem thousands of miles away -- it is a direct threat to our security at home and abroad," Cameron said.
Cameron earlier on Monday visited Paris, where he met President Francois Hollande and paid tribute outside the Bataclan concert venue, where 90 people were killed.
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"I firmly support the action President Hollande has taken to strike ISIL in Syria," Cameron said after talks in Paris.
"It's my firm conviction that Britain should do so too," he added.
In his speech to parliament, Cameron also announced details of "a significant new contingency plan" in case of attacks in Britain, which would include the rapid deployment of 10,000 military personnel to support the police.
Labour's anti-war leader Jeremy Corbyn is against any military action but Cameron appears increasingly confident that he can get enough support from Labour MPs to pass the vote, particularly after last week's UN Security Council resolution authorising countries to "take all necessary measures" against IS.
A Times/YouGov opinion poll last week found that 58 percent of people would approve of Britain joining air strikes on targets in Syria compared to 22 percent against.
Reports suggest the government could call a vote on the issue as early as the end of next week if ministers are confident of winning it.