Cameron promised to give the ethnic minorities more opportunities and power to make them feel they have "a real stake" in society.
The prime minister also used the speech to challenge the idea that Western meddling in the Middle East is to blame for the rise in extremism.
"Some argue it's because of historic injustices and recent wars, or because of poverty and hardship. This argument, what I call the grievance justification, must be challenged," he said, arguing that the root cause of the extremist threat is "the extremist ideology itself."
However, political observers warned that Cameron's speech could potentially ignite controversy among religious groups who may believe the new principles could be counter-productive and further alienate Muslim communities.
In response to Cameron's speech, the Muslim Council of Britain (MCB) said in a statement: "Challenging extremist ideology is what we all want, but we need to define tightly and closely what extremism is rather than perpetuate a deep misunderstanding of Islam and rhetoric, which inevitably facilitates extremists to thrive."
"We worry, however, that these latest suggestions will set new litmus tests which may brand us all as extremists, even though we uphold and celebrate the rule of law, democracy and rights for all.
Dissenting is a proud tradition of ours that must not be driven underground," the statement added.
"Above all we need to allow for real political issues to be discussed and debated robustly and not drive our youth underground for fear of being cast extremist," the MCB said.