They should look out for extremist material being distributed among children and target pupils with counselling, it is suggested.
Teachers are also encouraged to allow pupils to debate controversial topics such as the Iraq war - stopping frustrated young people turning to radical groups and crime.
The recommendations are contained in guidance due to be outlined by Ed Balls, the Schools Secretary.
A new "toolkit" will provide teachers with practical advice about how to deal with concerns over extremism in schools.
It comes amid fears that young people may be targeted by Islamist groups and right-wing organisations.
Earlier this year, Mr Balls admitted that a "very small number'' of pupils may already be at risk of radicalisation.
Chris Keates, general secretary of the NASUWT teachers' union, said: "We are living in challenging and difficult times which require concerted action if we are to overcome the threat of violent extremism, prejudice and bigotry."
He added: "There can be no doubt that extremist groups are seeking to target young people in order to recruit and exploit them for their pernicious purposes. Schools can make an important contribution in helping to prevent young people becoming the victims of extremism."
In June, the Government unveiled its new "Prevent" campaign designed to raise awareness of violent extremism in local areas, including schools, colleges, universities, community groups and religious organisations.
It said that education had a "key role" to play.
The document suggested schools should use the curriculum - particularly citizenship and religious education lessons - to help children discuss current affairs and links between different faiths.
It highlighted one programme in Oxford in which Muslim pupils could debate subjects such as Afghanistan, Iraq and the Sunni-Shia divide during their lunchtime.
Community and religious leaders - such as Imams - should be invited into schools to schools to take part in lessons, said the document.
And schools should also strike up partnerships with police, youth offending teams and local councils.
"If schools have concerns that a pupil may be being exposed to extremist material or influences, they can offer support through mentoring and by ensuring that the school is involved in the local partnership structures working on preventing violent extremism," said the report.
In a visit to a school in North London, Mr Balls was expected to endorse the guidance and provide further advice to teachers.
The National Union of Teachers backed the move, but insisted staff should not automatically be expected to report all concerns to police.
Christine Blower, acting general secretary, said: "For the objectives of Government guidance to be achieved, trust has to be maintained in schools. No teacher will ignore obvious information about a specific, real threat, but it is vital that teachers are able to discuss with and listen to pupils, without feeling that they have to report every word."
