A review of Sharia courts and a ban on fundamentalist clerics spreading bile-laden messages would be ordered if the Tories are re-elected, she said.
Extreme groups trying to infiltrate schools, universities, town halls and charities also will be rooted out.
Mrs May used her last major speech before the general election to underline her stance on the Islamist threat to British society.
She said: “We have been clear all along that the Government’s counter-extremism strategy must seek to defeat extremism in all its forms, but it’s obvious from the evidence that the most serious and widespread form of extremism we need to confront is Islamist extremism.
“Extremism is not something that can just be ignored.
"It cannot be wished away.
"It must be tackled head on.”
Laying out her wish list of counter-terrorism measures in an uncompromising speech, Mrs May called on British Muslims to help to tackle extremism.
She said: “To those who choose consciously to reject our values and the basic principles of our society, the message is equally clear – the game is up.
"We will no longer tolerate your behaviour.
"We will expose your hateful beliefs for what they are.” » | Anil Dawar | Tuesday, March 24, 2015
