The PM will tell the National Security Council a counter-extremism bill will be in the Queen’s Speech on 27 May reports BBC.
The bill will include new immigration rules, powers to close down premises used by extremists and “extremism disruption orders”.
Mr Cameron will say a “poisonous” extremist ideology must be confronted.
The proposals were first set out by Home Secretary Theresa May before the general election.
But the Conservatives were unable to secure the backing of their then Liberal Democrat coalition partners for the measures.
There is likely to be some opposition in the new Parliament on the grounds that some of the plans could infringe people’s right to free speech, BBC home affairs correspondent Danny Shaw said.
The measures are also expected to introduce banning orders for extremist organisations who use hate speech in public places, but whose activities fall short of it being proscribed as a terror group.
According to details given by Mrs May at last year’s Conservative Party conference, such orders would apply if ministers “reasonably believe” a group intended to incite religious or racial hatred, to threaten democracy, or if there was a pressing need to protect the public from harm, either from a risk of violence, public disorder, harassment or other criminal acts.
The granting of a ban, which would be subject to immediate review by the High Court, would make membership or funding of the organisation concerned a criminal offence.
The extreme disruption orders could be imposed on individuals, using the same criteria.