Ms Lucas said the Government’s counter-terrorism strategy Prevent should “be looked at again”.
But Marr hit out at the party co-leader’s stance and labelled it "knee-jerk liberalism".
Speaking on The Andrew Marr Show on the BBC, the presenter said: “Let me put it you that this is knee-jerk liberalism and one of the very few Muslim MPs in the last parliament, Khalid Mahmood, said this, ‘by and large the majority of the Muslim community have no real issue with Prevent.
“‘What we see is small groups of so-called activists who continue to condemn Prevent but provide no alternative’ and he’s talking really about people like you.”
Andrew Marr hit out at Caroline Lucas' stance on Prevent saying it was "knee-jerk liberalism"
Let me put it you that this is knee-jerk liberalism
Ms Lucas tried to stand her ground and said it should not necessarily be “scrapped” but “looked at again”.
“My position on Prevent is guided by the Muslim community that I speak to in my own constituency and who I speak to elsewhere,” she said.
“It’s about what is the most effective way of keeping people safe. When you have a programme that has lost credibility in vast areas of the Muslim society, then I think it means we should look at it again.
“It doesn’t mean scrapping it and not replacing it but it does certainly mean making sure we have a mechanism that has the confidence of the communities so we that can make sure we do our very best to keep people safe.”
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Hifsa Haroon-Iqbal, West Midlands regional Prevent leader, told the Asian Network presenter he needed to “get out of his studio”.
Host Nihal Arthanayake said finding a Muslim who supported Prevent, which aims to stop people becoming terrorists, was “as hard as finding hens' teeth”.
Speaking on the Asian Network’s Big Debate on the BBC, he said: “Do you know what, it’s as hard as finding hens' teeth, I’ve often thought when having conversations, to find a Muslim who actually does support Prevent.”