Home Secretary John Reid spoke at an emergency meeting of ministers and security officials and pressed for an urgent escalation in the propaganda war against such groups, the weekly said.
Reid said al Qaeda's "single extremist narrative" was becoming increasingly attractive to young Muslims in Britain, the broadsheet reported.
The Sunday Telegraph said it had been told by ministers that 30 terror plots were being probed and 1,500 young Muslims were suspects.
After the meeting on October 12, a minister said the foiled alleged terror plot to blow up trans-Atlantic aircraft had led Prime Minister Tony Blair to order a tougher stance.
"The approach is to bolster moderate voices and isolate and attack the extremists," the unnamed minister was quoted as saying.
Blair was reported to have told ministers to work with "the leaders, not the panderers" in the Muslim community.
The government has decided to fund an Islamic website calling for moderation, The Sunday Telegraph said.
And around 100,000 compact discs promoting moderation have been distributed free to Muslim students as an "antidote" to jihadist CDs circulating in universities, it added.
The Home Office told the newspaper: "It would not be appropriate to comment on meetings of this nature."

Copyright AFP (Agence France-Presse), 2006