The home secretary, Jacqui Smith, yesterday said the government's counter-terrorism strategy had to extend to challenging non-violent extremist groups that "skirt the fringes of the law ... to promote hate-filled ideologies".

Smith did not name them, but she urged local authorities and the police to tackle extremist groups that were targeting mosques and community centres to create the idea that being Muslim and being British were incompatible.

"They may not explicitly promote violence, but they can create a climate of fear and distrust where violence becomes more likely," she told a London conference of more than 700 local authority, police and community leaders discussing ways to prevent violent extremism.

"These are the groups that fail to speak out and condemn violence when any reasonable person would be outraged."

Smith added that both the far right and those "peddling their particular brand of antidemocratic ideology in the guise of religion" were "trying to create the idea that being Muslim and being British are incompatible". The home secretary said young Muslims were having to put up with threats, intimidation and general abuse and cited a case in Derby where an extremist group sought to take over a community centre.

Smith and the communities secretary, Hazel Blears, told the second annual conference on the government's programme to prevent violent extremism that a further £13.8m would be made available to disrupt radicalisers, challenge the rhetoric of extremists and support vulnerable individuals locally.

A project that identifies individuals at risk of getting swept up in violent extremism is also to be expanded. So far it has supported 100 individuals at two pilot sites in London and the north-west, and it is to be expanded so that it operates at 25 sites in 12 police force areas by next year.

Blears said that the programme to prevent violent extremism had so far reached more than 40,000 people since it started in April 2007.

She said that it was now time to "focus on the hard-edged debate", arguing that in some places local authorities had used the first year of the programme to understand the makeup of their communities, make the first links and build trust and confidence.

It was now important to move on to a debate that openly addressed the challenge of violent extremism: "In a small minority of cases, that's taking longer than it should. I recognise that it can be uncomfortable. In some cases it will take political leadership to get things moving. But it can and must be done," said Blears.