Cameron has been urging Britons to vote to remain in the union in a June 23 referendum, after striking a deal with European leaders to give the UK "special status" within the bloc if it remains.
"Britain will be out of the parts of Europe that do not work for us -- we will be permanently and legally protected from being a part of an ever-closer union," he said.
However, Britain would remain in "the driving seat of the world's biggest market," he said, and could "never be part of a European super-state."
The UK would be "stronger, safer and better off" in the EU, he said Monday, the first day of official campaigning for the referendum.
The threats faced by Britain and other European nations were real, said Cameron
, citing Russian aggression and Islamic terrorism.
"In my view, this is no time to divide the West," he said. "This is a time for strength in numbers."
London mayor supports 'Vote Leave'
Cameron's campaign appeared to meet stiff opposition when London's colorful, popular mayor, Boris Johnson, entered the debate on the side of the "Vote Leave" campaign Sunday.
Johnson announced his support for leaving the EU before a crowd of reporters Sunday afternoon, saying his decision to defy Cameron's position caused "a huge amount of heartache."
His intervention in the campaign appeared to have an immediate impact on the British pound when markets opened Monday, with the pound falling against all major currencies
At a news conference Sunday, Johnson laid out his position. "I will be advocating Vote Leave," he told reporters, "because I want a better deal for the people of this country, to save them money and to take back control."
His support will give the campaign to leave the EU a charismatic figurehead -- and will pit two of Britain's most powerful, influential politicians against each other as they attempt to convince Britons of the merits of their positions ahead of an "in or out" referendum on June 23
The men, both members of the ruling Conservative party, are former pupils of elite private school Eton and belonged to the same exclusive "dining club" during their days at Oxford University.
But high-ranking members of Cameron's Cabinet, including Justice Secretary Michael Gove, Culture Secretary John Whittingdale and Work and Pensions Secretary Iain Duncan Smith, have all come out in support of the "Vote Leave" campaign.
Cameron argues that the British economy -- the second-largest in the 28-nation bloc
-- will suffer if the country opts out.
In a 2,000-word opinion piece in The Telegraph on Sunday,
Johnson said leaving was a "once-in-a-lifetime chance to vote for real change."
"This is a moment to be brave, to reach out -- not to hug the skirts of Nurse in Brussels, and refer all decisions to someone else," he wrote.
Prime Minister: Let us stay
Before Johnson showed his hand, Cameron appeared on Sunday morning television
to push for a vote to stay.
"If Boris and if others really care about being able to get things done in our world, then the EU is one of the ways in which we get them done," he said.
"Having that seat at the table in the EU -- just as being a member of NATO
-- is a vital way that we project our values and our power and our influence in the world."
Britain is one of the biggest economies in the European Union and is a net contributor to the EU budget.
Critics say membership of the EU is a costly burden that brings regulations and excessive migration. Advocates say membership is good for the economy and leaving could be an expensive disaster.