“Our security and intelligence services have stopped something like seven attacks in the last six months, albeit attacks planned on a smaller scale” than Friday’s attacks in Paris, he told BBC Radio 4 from Turkey.
“We have been aware of these cells operating in Syria that are radicalizing people in our own countries, potentially sending people back to carry out attacks,” he added.
Security services have spent a “long time” working out how to deal with multiple coordinated attacks on the street, but will have to go “right back to the drawing board” after the Paris attacks, which killed at least 129 people.
“It was the sort of thing we were warned about,” said the prime minister.
Cameron added there were “hopeful signs” from Saturday’s talks in Vienna on Syria that progress was being made on how to deal with the Islamic State (IS), and that he was to speak with Russian Vladimir Putin later Monday.
“You can’t deal with so-called Islamic State unless you get a political settlement in Syria that enables you then to permanently degrade and destroy that organisation,” he said.
However, he repeated that any settlement must include the removal of Syrian President Bashar al-Assad, a sticking point between the West and Russia.
Britain is to recruit an extra 1,900 security and intelligence staff to counter the threat of terrorist violence following the Paris attacks, British media reported on Monday.
It would be “the biggest increase in British security spending since the 7/7 bombings in London” that killed dozens in 2005. The measures will be announced by Cameron later on Monday, according to the Guardian.
“I am determined to prioritise the resources we need to combat the terrorist threat because protecting the British people is my number one duty as prime minister,”Cameron will say, according to the newspaper.
He later told the BBC that Islamist terrorism was “the struggle of our generation.”
“This disease is a challenge we are going to have to face with everything we have got,” he said. “We will do everything we can to make sure we keep our people safe, but we live in a very, very dangerous world.”
The recruitment would increase the staff of intelligence agencies MI5, MI6 and GCHQ by some 15 percent, according to the Guardian and the Financial Times.
In addition, extra aviation security officers would assess airports around the world, in response to the crash of a Russian plane in Egypt last month that the British government suspects may have been downed by a bomb.
Britain is engaged in air strikes against IS in Iraq, but has not joined in the operation over Syria after parliament voted against it.
Cameron wants to extend the mission, but said first he needs to “build the argument and convince more people.”
When asked what ordinary citizens could do in face of the terror threat, the prime minister urged them to “be vigilant” but “remember our freedom depends on resolve and carrying on with our way of life.”