A standoff between the communities secretary, Hazel Blears, and the Muslim Council of Britain was said last night to "cut to the heart" of the government's revised counter-terror strategy to challenge those who defend terrorism and violent extremism.

Blears has suspended official links with the MCB over allegations that its deputy general secretary endorsed a Hamas call for attacks on foreign troops, including possibly British troops, if they try to intercept arms smuggled into Gaza.

Blears last night pressed the MCB for further clarification after it distanced itself from a declaration calling for a new jihad over Gaza made by the Hamas-backed "global anti-aggression campaign" in Istanbul last month. The cabinet minister is still pressing the MCB's deputy general secretary, Dr Daud Abdullah, who attended and signed the Istanbul declaration, to clarify his own position.

The dispute, involving a senior government minister and one of the most significant Muslim "umbrella" organisations, coincided with the launch of the Contest 2 counter-terror strategy and illustrated the determination of ministers to challenge radical views that fall short of support for violence but reject and undermine "our shared values".

Ministers have pulled back from spelling out a checklist of views that might constitute extremism. Instead, the Home Office strategy document published yesterday opts for a more low-key commitment to challenge those who "reject parliamentary democracy, dismiss the rule of law and promote intolerance and discrimination on the basis of race, faith, ethnicity, gender or sexuality".

The home secretary, Jacqui Smith, said yesterday the government had no intention of outlawing these views or criminalising those who held them: "Freedom of thought and speech are rights which are fundamental to our society. But we will not hear these views in silence. We should all stand up for our shared values and not concede the floor to those who dismiss then." At the Home Office launch of the revised strategy, Smith made it clear this extended to challenging those who voiced homophobic views in public.

The document also spells out that the new policy will be reflected in the groups that are supported and the projects that are sponsored as part of the £70m programme to prevent violent extremism.

But this failed to satisfy the Conservatives, with the shadow home secretary, Chris Grayling, claiming that ministers were still funding groups that "propagate extremism".

The revised counter-terror strategy contains fresh warnings about the likelihood of a "dirty bomb" attack in Britain, saying that changing technology and increased smuggling of chemical, radiological and biological materials make the prospect more realistic. It also discloses that counter-measures are being taken in Britain in anticipation of the possible importation of the use of roadside bombs and other improvised explosive devices from Iraq and Afghanistan.

The continued fragmentation of the al-Qaida organisation may lead to smaller, more autonomous networks but it predicts these new "self-starting" organisations will have access to new technology and may become capable of conducting more lethal operations.

Senior Whitehall officials acknowledged serious concern about the impact in Britain of the deteriorating situation in the Pakistan/Afghanistan borderlands, where al-Qaida groups have been involved in the direction and training of some terror cells in Britain. But the threat may diminish as "terrorism is subject to greater challenge in and by communities in this country, notably but not only by British Muslims, making it harder for terrorists to operate here and to recruit people to their cause".

The document also reflects more sophisticated thinking within MI5 about the process of radicalisation, making clear that the security services do not think there is a single cause or pathway to extremism. It acknowledges that political and economic grievances, including perceptions of British foreign policy in the Islamic world, have played a role, and that Iraq, Afghanistan and perceived inaction over Palestine have also contributed to anger and controversy.

But it notes that such grievances do not always or often lead to radicalisation, and that social and psychological factors are also important to the individual, often rooted in conflicts of identity. The strategy plays down the influence of radical preachers and instead talks of supportive peer groups and charismatic individuals as being crucial to the process of radicalisation. The strategy says that while many contemporary terrorist organisations purport to have religious objectives, many terrorists have little or no religious understanding or knowledge.

The implication of this analysis is that in addition to tough law enforcement operations, the counter-terrorism programme also engages with "vulnerable" individuals who are at risk of being recruited or have already been recruited by violent extremists.

Contest 2

• Those who defend terrorism and violent extremism to be challenged but not banned or prosecuted.

• New threat from "dirty bomb" as technology changes due to increased smuggling of chemical and biological materials.

• Al-Qaida fragmenting but "self-starting" successor groups may pose more lethal threat.

• Counter-terror budget to rise to £3.5bn a year by 2011.

Controversial statement: 'Obligations' to the people of Gaza

The Istanbul statement claims God has granted victory to Gazans over their "Zionist Jewish occupiers". But it also complains of an "international and local conspiracy" against Gaza, implicating Palestine leaders in the West Bank and accusing the Egyptian government of treason (though without mentioning it by name). The statement then sets out eight "obligations" for the Muslim community - "its religious scholars, its rulers and its peoples":

• To aid the people of Gaza in rebuilding "what the Zionist aggression destroyed"; to compensate the injured and support widows and orphans.

• In the delivery of aid and reconstruction, to deal only with Hamas.

• Not to recognise the Palestinian Authority as representative of the Palestinian people.

• To withhold aid from the undeserving or untrustworthy and to punish those who cause "mayhem, negligence and waste" of funds.

• To find a fair formula for reconciliation "between the sons of the Palestinian people" (ie Fatah and Hamas), so as to establish a legitimate authority that will "carry on with jihad and resistance against the occupier until the liberation of all Palestine".

• To open all crossings in and out of Palestine, giving the Palestinians access to "money, clothing, food, medicine, weapons and other essentials".

• To regard all those who contribute substantially to the "crimes and brutality" of Israel in the same way as Israel itself.

• To reject and "fight by all means" the sending of foreign warships into Muslim waters on the basis of "claiming to control the borders and prevent the smuggling of arms to Gaza".