Hazel Blears has said there will be "far more" work with Muslim communities to tackle radicalism, but ruled out talking to the most extreme groups.
Ten years after US embassy bombings in Africa, the communities secretary said she wanted to help angry young people channel anger through democratic means.
But it was not right for ministers to engage with those who justified suicide bombing or the destruction of Israel.
A leading de-radicaliser says ministers should listen more to their grievances.
As ceremonies mark the 10th anniversary of attacks on embassies in Kenya and Tanzania, BBC security correspondent Frank Gardner said al-Qaeda's violent tactics had come under mounting criticism from Islamist scholars who had previously supported it.
'Vent frustration'
But former jihadi Hanif Qadir, who tries to steer young men in east London away from violence said the number of young British Muslims attracted to violent extremism was growing.
He added that, without more "critical dialogue" between the government and young Muslims, they would go on to vent their frustration elsewhere.
Speaking to BBC Radio 4's Today programme, Ms Blears said she was pleased it appeared the "theological base" for al-Qaeda in Afghanistan and Pakistan was "beginning to fragment".
Part of the challenge is how do we ensure that those young people who are angry about injustice, about poverty, about all of those things, how do we ensure that they can channel some of that anger through democratic means
Hazel Blears
Communities Secretary
"Getting to the theological base, as well as doing the political work with young people, is the way forward for us," she said.
Ms Blears said she wanted to engage with groups which condemned violent extremism - even if they "wouldn't necessarily hold views on foreign policy that are not identical to the government".
But asked whether she would consider talking to the most extreme groups, she said: "I think if you have got groups that are actively promoting violent extremism, groups that are on record as saying Israel should be wiped off the face of the map, justifying suicide bombing, then I don't think it is right for ministers to be engaging with them, sharing platforms and giving them credibility."
Instead she pledged to do "far more work on the ground" with Muslim communities over the next three years and work to persuade young people there were other ways to protest.
"Part of the challenge is how do we ensure that those young people who are angry about injustice, about poverty, about all of those things, how do we ensure that they can channel some of that anger through democratic means," she said.
"That's part of my task, to try and build the voices of young Muslims, of women, to make sure that they have more representation in public life and they actually do feel that the democratic systems work for them."
Among recent announcements by the government have been £12.5m for Muslim communities to fund projects which aim to "undermine extremist ideology" and funding for a board of Islamic theologians to debate issues affecting Muslims in the UK.
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