The UK will no longer tolerate the behaviour of Islamist extremists who "reject our values", Theresa May says.
The home secretary said a future Tory government would introduce measures such as "closure orders" to shut premises owned or used by extremists.
She also said there were plans for civil "extremism disruption orders" that could be used against individuals.
Shadow home secretary Yvette Cooper said there was a "massive gap between rhetoric and reality".
Mrs May also said everyone in Britain had "responsibilities as well as rights", and must respect laws and institutions. A "partnership" of individuals and communities could tackle the issue, she added.
Other measures she said would be introduced if the Conservatives won the general election included:
- "banning orders" for groups which do not reach the current threshold to be outlawed under terrorism laws
- a "positive campaign to promote British values" to the public
- a review of supplementary schools, which are currently unregulated
- HM Inspectorate of Constabulary reviewing how police forces have responded to "honour crimes", female genital mutilation and forced marriage
- new "extremism officer" roles in prisons to deal with extremist inmates and gangs
- a "full review of citizenship law" to make sure successful applicants respect British values
- a "sharp reduction" in funding for translation services and a "significant increase" in money for English language training
By Danny Shaw, BBC home affairs correspondent
"The game is up," said Theresa May. The phrase has echoes of an address 10 years ago - by Tony Blair.
That was a message to Islamist extremists, a month after four suicide bombers had murdered 52 people in the 7/7 London attacks.
Like Mrs May, Mr Blair outlined measures to deal with people who threaten British values, including considering widening the grounds for banning extremist groups and strengthening citizenship rules.
The former Labour prime minister got some of his proposals through, but others foundered. The current Conservative home secretary may also find obstacles on the road to turning rhetoric into reality.
Mrs May, who set out many of these proposals in her September party conference speech, also announced plans for a review of Sharia courts - Islam's legal system - in England and Wales, to examine whether they are compatible with British values.
She said there was "increasing evidence that a small but significant number of people living in Britain - almost all of whom are British citizens - reject our values".
She said "hundreds" of British citizens had travelled to fight in Syria and Iraq and raised concerns about the "Trojan Horse plot" in Birmingham. Last week a committee of MPs said that apart from one incident in one school "no evidence of extremism or radicalisation was found by any of the inquiries in any of the schools involved".
And Mrs May said the government wanted to defeat extremism in "all its forms", but said "the most serious and widespread form of extremism we need to confront is Islamist extremism".
Ms Cooper said while the principles of Mrs May's proposals were "the right ones", she questioned the absence of "policies to back those principles up".
She said Labour's plans included a "major overhaul" of the Prevent programme - a multi-agency programme which aims to stop people being drawn into terrorist-related activity - and a review of all serious terror suspect cases to see whether relocation powers should be used.
By Norman Smith, BBC assistant political editor
Theresa May hopes her call to "tackle head on" Islamist extremism will be taken as a wake-up call to voters, some of whom she believes have been unwilling to stand up for British values.
But Mrs May also wants her speech to be a wake-up call to some minority communities.
And very lastly, Mrs May perhaps wants her speech to be a wake-up call to her party.
A reminder of the sort of hard headed, traditional Conservatism she might offer as a potential leader after David Cameron.
Chairman of the Muslim Forum think tank, Manzoor Moghal, told the BBC's World At One Mrs May's proposals would infringe people's freedom of speech, saying: "We might be sleep walking into what would be like a police state."
He also said Sharia courts "do not contradict British laws" and were "subservient to British laws all the time".
But Raffaello Pantucci, director of International Security Studies at the Royal United Services think tank, disagreed that the nation was moving towards infringing civil liberties, saying distinguishing between extremists and conservatives was "very difficult".
"The fundamental problem here is that you're trying to deal with a group of people who are being very careful about what they say and how they say it," he added.