The speech came a day after Cameron said in an interview on the American television network NBC that he wanted his country to do more in the fight against jihadi terrorism and to create what he called "a full-spectrum response."
And it came less than four weeks after a gunman went on a murderous rampage on a beach in Tunisia
, killing 38 people -- 30 of them British.
Monday's speech focused on fighting the extremist ideology that he said leads to violence and finding ways to increase the sense of inclusion felt by young people in different British communities.
"For all our successes as a multiracial, multifaith democracy, we have to confront a tragic truth that there are people born and raised in this country who don't really identify with Britain -- and feel little or no attachment to other people here," Cameron said.
"So when groups like ISIL seek to rally our young people to their poisonous cause, it can offer them a sense of belonging that they lack here at home."
ISIL is another acronym for ISIS
, the self-proclaimed Islamic State in Iraq and Syria terrorist group.
Study on boosting inclusion to be announced
The Prime Minister also laid out other elements of his government's five-year plan to fight terrorism at home. The measures included making it legal for parents to confiscate the passports of children they fear might travel to Syria
, allocating money to groups that will help spread an "alternative narrative," tougher regulation of foreign TV channels that promote messages of hate, and taking steps to reduce segregation in schools and housing.
Cameron also announced that he was appointing Louise Casey, a government official who has worked on various social welfare issues, to investigate how to boost opportunity and integration for those in Britain who feel left out.
"We need young people to understand that here in the UK, they can shape the future by being an active part of our great democracy," he said.
But his speech drew skepticism from some in Britain's Muslim community.
"The Prime Minister's speech today has once again failed to engage the Muslim community, and he has peddled the same lines which we have seen from politicians since 2001," Mohammed Shafiq, chief executive of the Ramadhan Foundation, said in a statement. The foundation, based in Manchester, in northern England, says its goal is to bring attention to the educational and welfare needs of the Muslim community.
"In terms of ISIS, we are in total agreement with the Prime Minister, they are a barbaric and evil entity and their ideology of violence is what we must confront," Shafiq's statement said. "They have distorted Islamic teaching
to suit their agenda, and we as Muslims must be doing more to confront them."
But he continued, "Successive governments have also conflated security/extremism with integration and cohesion which I believe is the wrong debate. If Louise Casey will seriously listen and understand the concerns of British Muslims, then we are prepared to work with her; if it is not, this will be another failed government exercise."
Too often, Shafiq said, ordinary citizens are penalized, snooped on and deprived of their civil liberties in the name of fighting terrorism.
'The sick and brutal reality of ISIL'
For his part, Cameron said that young British Muslims must be disabused of their misconceptions about ISIS.
"If you are a boy, they will brainwash you, strap bombs to your body and blow you up," he said. "If you are a girl, they will enslave and abuse you.
"That is the sick and brutal reality of ISIL."