The Senate security and defence committee also recommends creation of a "wanted terrorist" list and urges the government to explore options for training and certification of imams in Canada.
In addition, it calls on the government to work with Muslim communities to create "an effective counter-narrative" to denounce the ideology of Islamist fundamentalism.
In general, the senators express concern about the small number of terrorism prosecutions, including for extremist financing.
"We cannot try to appease this threat that we face," Conservative Sen. Daniel Lang, the committee chairman, said in an interview.
The committee's 25 recommendations flow from nine months of hearings on security threats facing Canada. The interim report examines terrorist recruitment, operations, financing, prosecutions and other aspects of what it calls the genuine threat of violent extremism.
Committee members were told 93 Canadians had sought to join Islamist extremist groups like the Islamic State of Iraq and the Levant, al-Qaida and Boko Haram.
Canadians must tackle the issue in a thoughtful, balanced way without undermining the values "that make us great," the report says.
"We must find every resource, tool and technique available to us as a civilized society to diminish and defeat a most uncivilized force," the senators say. "Our goal is to lessen the risk to all Canadians, including the risk to vulnerable young Canadians who might be lured to extreme ideas and violent action."
A number of the report's recommendations push farther than the Harper government chose to go in its controversial omnibus security bill, introduced after two Canadian soldiers were killed last October in daylight attacks just days apart by jihadi-inspired, lone-wolf attackers.
For instance, the anti-terrorism bill — which recently received royal assent — makes it a crime to promote terrorist acts but stops short of outlawing the glorification of extremist plots and symbols.
The report represents the views of the Conservative majority on the committee, but lacks the backing of Liberal members.
Liberal Sen. Grant Mitchell, the committee's deputy chairman, said Wednesday he disagreed with the Conservatives on several key issues. Mitchell supports police counselling and liaison to help steer young people away from radical ideas — an approach the report questions.
Mitchell said he also wanted to see another $100 million for the RCMP, continuation of a federal research program on the roots of terrorism, and a more balanced approach to the problem of right-wing racist extremism.
Police had told the senators that outreach, including counselling and community liaison, were preferred means of dealing with fundamentalist threats.
"The effect of these options is unclear and unproven," the report says.
Peace bonds, which can restrict the movement of terror suspects, offer only a "limited solution," it adds.
"Law enforcement and the Public Prosecution Service must work harder to bring cases before the courts so the accused can have a fair hearing and the evidence can be tested."
The committee says some foreign-trained imams have been spreading extremist religious ideology and messages that are not in keeping with Canadian values, contributing to radicalization. It calls on the government to work with the provinces and Muslim communities to "investigate the options that are available for the training and certification of imams in Canada."
Another recommendation takes aim at groups that invite foreign nationals with extremist views to speak to impressionable youth. It urges the government to establish a publicly accessible list of "ideological radicals" deemed to be a security threat, prohibiting them from visiting Canada.
A spokesman for Public Safety Minister Steven Blaney defended the government's efforts to date, noting the anti-terrorism legislation allows police to take action to prevent radicalization, including removal of Internet material used to influence people.
Follow @JimBronskill on Twitter
Also on HuffPost