Home Secretary John Reid has described as "a dreadful misjudgement" an open letter in which Muslim groups criticise British foreign policy.
MPs Sadiq Khan and Mohammed Sarwar at a meeting with the PM
The letter, signed by three Muslim MPs, three peers and 38 groups, suggested some policies provoked terrorists acts.
Mr Reid said no competent government would remain in power if policies were "dictated by terrorists".
Echoing this stance, former Tory leader Michael Howard said the letter had given "ammunition" to extremists.
He said: "It is, I think, completely misconceived to suggest that we should change our foreign policy because it might cause some people to take up arms against us.
"That's a form of blackmail and I think that letter was completely misconceived."
The letter pointed to the "debacle" of Iraq and the UK's stance over the Middle East crisis as examples of policies which fuelled extremism.
Downing Street said Tony Blair "stands ready" to meet Muslim representatives when he returns to the UK.
The letter urges the prime minister to redouble his efforts to tackle terror and extremism, and change foreign policy to show that the UK values the lives of civilians.
MP Sadiq Khan, who was among those who signed the letter, said British foreign policy was seen by many as unfair and unjust.
"Whether we like it or not such a sense of injustice plays into the hands of extremists," he said.
"As moderates we will do all we can to fight extremism. We hope the government will join us in this, not just by changing the rules on hand luggage, but by showing itself as an advocate for justice in the world."
Ajmal Masroor, from the Islamic Society of Britain, which represents second-generation Muslims, maintained the war in Iraq was why the UK is facing a terrorist threat.
"The letter itself is very well written and very reflective of the sentiment of Muslims," said Mr Masroor.
"Muslims are saying Islam and the Muslim communities did not give rise to extremism, and did not radicalise the young people."
Desire for democracy
The home secretary said he would not question the motives of those who signed the letter, but said it was a "dreadful misjudgement if they believe that the foreign policy of this country should be shaped in part or in whole under the threat of terrorist activity".
Mr Reid told the BBC: "No government worth its salt would stay in power in my view, and no government worth its salt, would be supported by the British people if our foreign policy or any other aspect of policy was being dictated by terrorists.
"That is not the British way, it is antithetical to our very central values. We decide things in this country by democracy, not under the threat of terrorism."